# Math Homework Help

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• Math
We have to evaluate the integral \int_{0}^{1}cosh(t)dt  We know that the integral of cosh(t) = sinh(t) . Therefore we can write, \int_{0}^{1}cosh(t)dt=[sinh(t)]_{0}^{1}...

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• Math
You need to evaluate the definite integral using the fundamental theorem of calculus, such that: int_a^b f(x) dx = F(b) - F(a) int_(1/(sqrt3))^(sqrt 3) 8/(1+x^2) dx = 8 int_(1/(sqrt3))^(sqrt 3)...

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• Math
You need to evaluate the definite integral using the fundamental theorem of calculus, such that: int_a^b f(u) du = F(b) - F(a) int_1^2 (4+u^2)/(u^3) du = int_1^2 4/(u^3) du + int_1^2 (u^2)/(u^3)...

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• Math
int_(-1)^1 e^(u+1)du To evaluate this, apply the formula int e^x dx = e^x . = e^(u+1) |_(-1)^1 Then, plug-in the limits of the integral as follows F(x) =int_a^b f(x)dx=F(b)-F(a) ....

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• Math
Hello! This integral is a table one, int((4)/(sqrt(1-x^2)))dx=4arcsin(x)+C. Therefore the definite integral is equal to 4*(arcsin(1/sqrt(2))-arcsin(1/2))=4*(pi/4-pi/6)=4*pi/12=pi/3 approx 1.047.

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• Math
You need to evaluate the definite integral using the fundamental theorem of calculus such that int_a^b f(x)dx = F(b) - F(a) int_(pi/6)^pi sin theta d theta = -cos theta|_(pi/6)^pi...

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• Math
Evaluate int_-5^5(e)dx Please note that e is a constant approximately equal to 2.718. Integrate the function. =ex Evaluate the function from x=-5 to x=5. =e(5)-e(-5)=5e+5e=10e =27.183

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• Math
int_0^1(u+2)(u-3)du =int_0^1(u^2-3u+2u-6)du =int_0^1(u^2-u-6)du =[u^3/3-u^2/2-6u]_0^1 =[1^3/3-1^2/2-6*1]-[0^3/3-0^2/2-6*0] =(1/3-1/2-6) =(2-3-36)/6 =-37/6

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• Math
Evaluate int_0^4(4-t)(sqrt(t))dt =int_0^4(4t^(1/2)-t^(3/2))dt Integrate the function. inta^n=a^(n+1)/(n+1) =(4t^(3/2))/(3/2)-t^(5/2)/(5/2)=(8/3)t^(3/2)-(2/5)t^(5/2) Evaluate the...

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• Math
Hello! Find the indefinite integral first: int((x-1)/sqrt(x))dx=int(x^(1/2)-x^(-1/2))dx=(2/3)*x^(3/2)-2*x^(1/2)+C. So the definite integral is equal to...

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• Math
int_0^2 (y-1)(2y+1)dy Before evaluating, expand the integrand. =int_0^2 (2y^2+y-2y-1)dy =int_0^2(2y^2-y-1)dy Then, apply the integral formulas int x^n dx=x^(n+1)/(n+1) and int cdx = cx ....

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• Math
int_0^(pi/4) sec^2(t) dt Take note that the derivative of tangent is d/(d theta) tan (theta)= sec^2 (theta). So taking the integral of sec^2(t) result to: = tan (t) |_0^(pi/4) Plug-in the...

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• Math
int_0^(pi/4) (sec (theta) tan (theta)) d theta Take note that the derivative of secant is d/(d theta) (sec (theta)) = sec(theta) tan (theta) . So taking the integral of sec(theta) tan(theta)...

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• Math
int_1^2(1+2y)^2dy =int_1^2((1)^2+2*2y*1+(2y)^2)dy =int_1^2(1+4y+4y^2)dy =[y+4y^2/2+4y^3/3]_1^2 =[y+2y^2+(4y^3)/3]_1^2 =[2+2(2)^2+(4(2^3))/3]-[1+2(1)^2+(4(1)^3)/3]...

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• Math
int_1^4(5-2t+3t^2)dt apply the sum rule and power rule, =[5t-2t^2/2+3t^3/3]_1^4 =[5t-t^2+t^3]_1^4 =[5*4-4^2+4^3]-[5*1-1^2+1^3] =(20-16+64)-(5-1+1) =(84-16)-(5) =63

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• Math
int_0^4(1+(1/2)u^4+(2/5)u^9)du =[u+(1/2)(u^(4+1)/(4+1))+(2/5)(u^(9+1)/(9+1))]_0^4 =[u+u^5/10-u^10/25]_0^4 [1+1^5/10-1^10/25]-[0+0^5/10-0^10/25] =(1+1/10-1/25) =(50+5-2)/50 =53/50

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• Math
You need to evaluate the definite integral such that: int_1^9 sqrt x dx = (x^(3/2))/(3/2)|_1^9 int_1^9 sqrt x dx = (2/3)(9sqrt9 - 1sqrt1) int_1^9 sqrt x dx = (2/3)(27-1) int_1^9 sqrt x dx...

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• Math
Evaluate int_1^8(x^(-2/3))dx Integrate the function. inta^n=a^(n+1)/(n+1) =x^(1/3)/(1/3)=3x^(1/3) Evaluate the function from x=1 to x=8. =3[8^(1/3)-1^(1/3)] =3[2-1] =3

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• Math
Hello! Part 1 of the Fundamental Theorem of Calculus states that for a continuous function f F'_a(x)=f(x), where F_a(x)=int_a^xf(t)dt. Here f(t)=sqrt(t^2+4) and g(x)=F_0(x)....

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• Math
Hello! Part 1 of the Fundamental Theorem of Calculus states that for a continuous function f F'_a(x)=f(x), where F_a(x)=int_a^xf(t)dt. Here f(t)=ln(t) and h(x)=F_1(e^x). Therefore...

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• Math
Hello! Part 1 of the Fundamental Theorem of Calculus states that for a continuous function f F'_a(x)=f(x), where F_a(x)=int_a^xf(t)dt. Here f(t)=t^2/(t^4+1) and h(x)=F_1(sqrt(x))...

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• Math
Hello! Part 1 of the Fundamental Theorem of Calculus states that for a continuous function f F'_a(x)=f(x), where F_a(x)=int_a^xf(t)dt. Here f(t)=cos^2(t) and y(x)=F_0(x^4). Therefore...

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• Math
You need to evaluate the integral, such that: int_(-1)^2(x^3 - 2x)dx = int_(-1)^2 x^3 dx - int_(-1)^2 2x dx int_(-1)^2(x^3 - 2x)dx = (x^4/4 - x^2)|_(-1)^2 int_(-1)^2(x^3 - 2x)dx = (2^4/4 - 2*2...

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• Math
int_(-1)^1 x^100 dx To evaluate this, apply the formula int x^n dx = x^(n+1)/(n+1) . = x^101/101 |_(-1)^1 Then, plug-in the limits of the integral as follows F(x) =int_a^bf(x) dx = F(b)-...

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• Math
Hello! Part 1 of the Fundamental Theorem of Calculus states that for a continuous function f F'_a(x)=f(x), where F_a(x)=int_a^xf(t)dt. Here f(t)=1/(t^3+1) and g(x)=F_1(x). Therefore...

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• Math
Hello! Part 1 of the Fundamental Theorem of Calculus states that for a continuous function f F'_a(x)=f(x), where F_a(x)=int_a^xf(t)dt. Here f(t)=e^(t^2-t) and g(x)=F_3(x). Therefore...

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• Math
Hello! Part 1 of the Fundamental Theorem of Calculus states that for a continuous function f F'_a(x)=f(x), where F_a(x)=int_a^xf(t)dt. Here f(t)=(t-t^2)^8 and g(x)=F_5(x). Therefore...

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• Math
2-4+6-8+10-12+14- ...+210 To compute this, group the positive numbers and group the negative numbers together. In getting the sum of the negative numbers, consider the last negative term. =...

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• Math
To take the sum of -i and i, the operation that should be performed is addition. -i + i To add like terms, add the coefficients and copy the variable. Since there are no written numbers at the...

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• Math
We are asked to find the circumcenter and orthocenter for triangle ABC with vertices at A(5,7),B(0,2) and C(1,1). (1) The circumcenter is the intersection of the perpendicular bisectors of the...

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• Math
You need to use the mean value theorem such that: int_a^b f(x)dx = (b-a)f(c), c in (a,b) int_(-1)^1 sqrt(1+x^2)dx = (1+1)f(c) = 2f(c) You need to verify the monotony of the function f(x) =...

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• Math
You need to use the mean value thorem to verify the given inequality, such that: int_a^b f(x)dx = (b-a)*f(c), c in (a,b) Replacing cos x for f(x) and pi/6 for a, pi/4 for b, yields:...

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• Math
int_-3^0(1+sqrt(9-x^2))dx Consider the graph of y=f(x)=1+sqrt(9-x^2) y=1+sqrt(9-x^2) y-1=sqrt(9-x^2) (y-1)^2=9-x^2 x^2+(y-1)^2=3^2 This is the equation of circle of radius 3 centred at...

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• Math
int_-5^5(x-sqrt(25-x^2))dx =int_-5^5xdx-int_-5^5sqrt(25-x^2)dx =I_1-I_2 I_1 can be be interpreted as area of two triangles;one above the x-axis and the other below axis.Since they are on the...

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• Math
int_(-1)^2 |x| dx To interpret this in terms of area, graph the integrand. The integrand is the function f(x) =|x|. Then, shade the region bounded by the graph of f(x)=|x| and the x-axis in the...

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• Math
int_0^10 |x-5|dx To interpret this in terms of area, graph the integrand. The integrand is the function f(x) = |x - 5|. Then, shade the region bounded by f(x) = |x-5| and the x-axis in the...

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• Math
You need to use the mean value thorem to verify the given inequality, such that: int_a^b f(x)dx = (b-a)*f(c), c in (a,b) Replacing x^2 - 4x + 4 for f(x) and 0 for a, 4 for b, yields: int_0^4...

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• Math
You need to check if int_0^1 sqrt(1+x^2)dx <= int_0^1sqrt(1+x)dx , using mean value theorem, such that: int_a^b f(x)dx = (b-a)f(c),  where c in (a,b) int_0^1 sqrt(1+x^2)dx <=...

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• Math
You need to use the midpoint rule to approximate the interval. First, you need to find Delta x , such that: Delta x = (b-a)/n The problem provides b=8, a=0 and n = 4, such that: Delta x =...

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• Math
You need to use the midpoint rule to approximate the interval. First, you need to find Delta x, such that: Delta x = (b-a)/n The problem provides b=pi/2 , a=0 and n = 4, such that: Delta x =...

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• Math
You need to use the midpoint rule to approximate the interval. First, you need to find Delta x , such that: Delta x = (b-a)/n The problem provides b=2, a=0 and n = 5, such that: Delta x =...

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• Math
You need to evaluate the definite integral using the mid point rule, hence, first you need to evaluate Delta x: Delta x = (b-a)/n => Delta x = (5-1)/4 = 1 You need to denote each of the 4...

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• Math
You need to use the fundamental theorem of calculus, to prove the equality, such that: int_a^b f(x)dx = F(b) - F(a) You need to replace x for f(x), such that: int_a^b xdx = x^2/2|_a^b int_a^b...

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• Math
You need to evaluate the definite integral, such that: int_a^b f(x) dx = F(b) - F(a) int_a^b x^2 dx = (x^3)/3|_a^b int_a^b x^2 dx = (b^3)/3 - (a^3)/3 int_a^b x^2 dx = (b^3 - a^3)/3 Hence,...

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• Math
You have to recall the definition of the Reiman Integral int_a^bf(x)dx=lim_(n->oo)sum_(i=1)^nf(x(i))Deltax where Deltax =(b-a)/n and x(i)= a +iDeltax x  a=2 and b = 6  Deltax = (6-2)/n=...

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• Math
int_1^10 (x-4ln(x))dx To express this definite integral as limit of Riemann's Sum, apply the formula: int_a^b f(x) dx = lim_(n-> oo)sum_(i=1)^oo f(x_i)Delta x where Delta x = (b-a)/n x_i...

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• Math
int_-1^2(1-x)dx To interpret the integral in terms of area , graph the integrand. The integrand is the function f(x)=1-x Graph the function in the interval (-1,2). Refer the attached graph. The...

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• Math
int_0^9 (1/3x-2)dx To interpret this integral in terms of area, graph the integrand. The integrand is the function f(x)=1/3x-2 . Then, shade the region bounded by f(x)=1/3x-2 and the...

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• Math
v(t)=2t-1/(1+t^2) position of the particle s(t) is given by, s(t)=intv(t)dt s(t)=int(2t-1/(1+t^2))dt s(t)=2(t^2/2)-arctan(t)+C , C is constant s(t)=t^2-arctan(t)+C Now let's find C ,...

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a(t) = sin(t) + 3cos(t) v(t) = -cos(t) + 3sin(t) + a Now, v(0) = 2 Thus, 2 = -cos(0)+3sin(0)+a or, 2 = -1 + 0 + a or., a = 3 Now, v(t) = -cos(t) + 3sin(t) + 3 Thus, s(t) = -sin(t) -...