# Homework Help

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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_(-2)^0 ((1/2)t^4 + (1/4)t^3 - t)dt = int_(-2)^0...

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• Math
We will use linearity of integral: `int(a cdot f(x)+b cdot g(x))dx=a int f(x)dx+b int g(x)dx.` `int_0^3(1+6w^2-10w^4)dw=int_0^3dw+6int_0^3w^2dw-10int_0^3w^4dw=`...

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• Math
You need to use the following substitution to evaluate the definite integral, such that: `1 - t = u => -dt = du` `int_(-1)^1 t*(1-t)^2dt = int_(u_1)^(u_2) (1 - u)*u^2 (-du)` `int_(u_1)^(u_2) (u...

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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_0^pi (5e^x+ 3sin x)dx = int_0^pi 5e^x dx + int_0^pi 3sin x...

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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_1^2 (1/x^2 - 4/x^3)dx = int_1^2 1/x^2 dx - int_1^2 4/x^3 dx`...

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• Math
`int_1^4(4+6u)/sqrt(u)du` `=int_1^4(4/sqrt(u)+(6u)/sqrt(u))du` `=int_1^4(4u^(-1/2)+6u^(1/2))du` `=[4(u^(-1/2+1)/(-1/2+1))+6(u^(1/2+1)/(1/2+1))]_1^4` `=[4(u^(1/2)/(1/2))+6(u^(3/2)/(3/2))]_1^4`...

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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_0^4(3sqrt t - 2e^t)dt = int_0^4 3sqrt tdt - int_0^4 2e^t...

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• Math
You need to evaluate the definite integral, such that: `int_0^1 x(root(3) x + root(4) x)dx = int_0^1 (x^(1+1/3) + x^(1+1/4))dx` `int_0^1 x(root(3) x + root(4) x)dx = ((x^(2+1/3))/(2+1/3) +...

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• Math
You need to evaluate the indefinite integral, such that: `int f(x)dx = F(x) + c` `int (x^2 - x^(-2))dx = int (x^2)dx - int x^(-2) dx ` Evaluating each definite integral, using the formula `int x^n...

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• Math
`int sqrt(x^3)root(3)(x^2) dx` Before evaluating, convert the radicals to expressions with rational exponents. `= int x^(3/2)*x^(2/3) dx` Then, simplify the integrand. Apply the laws of exponent...

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• Math
`int (x^4-1/2x^3+1/4x-2)dx` To evaluate this integral, apply the formulas `int x^n dx=x^(n+1)/(n+1) +C` and `int adx = ax + C` . `int (x^4-1/2x^3+1/4x-2)dx` `=x^5/5 - 1/2*x^4/4 + 1/4*x^2/2-2x...

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• Math
`int (y^3+1.8y^2-2.4y)dy` To evaluate this integral, apply the formula `int x^n dx = x^(n+1)/(n+1) + C` . `= y^4/4 + 1.8y^3/3 - 2.4y^2/2 + C` `=0.25y^4 + 0.6y^3 - 1.2y^2 + C` Therefore, `...

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• Math
You need to evaluate the indefinite integral, hence, you need to open the brackets, such that: `(u+4)(2u+1) = 2u^2 + 9u + 4` `int (u+4)(2u+1) du = int (2u^2 + 9u + 4) du ` `int (u+4)(2u+1) du =...

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• Math
`intv(v^2+2)^2dv` `=intv((v^2)^2+2v^2*2+2^2)dv` `=intv(v^4+4v^2+4)dv` `=int(v^5+4v^3+4v)dv` apply the power rule, `=v^6/6+4v^4/4+4v^2/2+C` , C is constant `=v^6/6+v^4+2v^2+C`

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• Math
`int(x^3-2sqrt(x))/xdx` ``Simplify by dividing each term in the numerator by x. ` <br> ` `=(x^3/3)-(2x^(1/2))/(1/2)+C` `=(x^3/3)-4x^(1/2)+C` `` ` `

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• Math
`int(x^2+1+1/(x^2+1))dx` apply the sum rule, `=intx^2dx+int1dx+int1/(x^2+1)dx` To evaluate the above integrals, we know that, `intx^ndx=x^(n+1)/(n+1)` and `int1/(x^2+1)dx=arctan(x)` using above,...

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• Math
`int(csc^2(t)-2e^t)dt` Apply the sum rule, `=intcsc^2(t)dt-int(2e^tdt` We now the following common integrals, `intcsc^2(x)=-cot(x)` and `inte^xdx=e^x` evaluate using the above, `=-cot(t)-2e^t+C`...

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• Math
You need to evaluate the indefinite integral, such that: `int f(theta)d theta = F(theta) + c` `int (theta - csc theta* cot theta)d theta = int theta d theta - int (csc theta* cot theta)d theta`...

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• Math
`g(x)=int_(2x)^(3x)(u^2-1)/(u^2+1)du` `g(x)=int_(2x)^0(u^2-1)/(u^2+1)du+int_0^(3x)(u^2-1)/(u^2+1)du` `g(x)=-int_0^(2x)(u^2-1)/(u^2+1)du+int_0^(3x)(u^2-1)/(u^2+1)du`...

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• Math
`F(x)=int_x^(x^2)(e^(t^2))dt` From the fundamental theorem of calculus, `int_x^(x^2)(e^(t^2))dt=F(x^2)-F(x)` `d/dxint_x^(x^2)(e^(t^2))dt=F'(x^2).d/dx(x^2)-F'(x)` `=2x(e^((x^2)^2))-e^(x^2)`...

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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_0^3 (2sin x - e^x) dx =int_0^3 2sin x dx - int_0^3 e^x dx`...

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• Math
`int_1^2((v^3+3v^6)/v^4)dv` simplify the integrand and apply the sum rule, `=int_1^2(v^3/v^4+(3v^6)/v^4)dv` `=int_1^2(1/v+3v^2)dv` using the following common integrals `int1/xdx=ln(x)` and...

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• Math
Evaluate `int_1^18(3/z)^(1/2)dz` `=int_1^18sqrt(3)z^(-1/2)dz` `=sqrt(3)int_1^18z^(-1/2)dz` Integrate the function. `=sqrt(3)[z^(1/2)/(1/2)]=sqrt(3)[2z^(1/2)]` Evaluate the function from 1 to...

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• Math
`int_0^1 (x^e+e^x)dx` To evaluate this, apply the formulas `int u^ndu = u^(n+1)/(n+1)` and `int e^udu=e^u` . `= (x^(e+1)/(e+1) + e^x) |_0^1` Then, plug-in the limits of integral as follows...

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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
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
`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
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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• History
There are many different ways to answer this question. Let us look at a few. One way to answer this is to say that Thanksgiving is celebrated as a way of emulating the Pilgrims who were some of...

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• Politics
The problem with defining the term "extremist political organization" is that it is by nature one applied only in the second or third person. In other words, the word "extremism" is one we do not...

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• Social Sciences
Compatibilism attempts to resolve the problem of free will and determinism by proposing that the two positions are compatible. Specifically, it asserts that: Determinism is true, that is, all human...

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• History
Lincoln's Thanksgiving Proclamation, which declared the final day of November a national day of "thanksgiving and praise to Almighty God," was one of many similar declarations by American...

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• Health
To evaluate an article from the perspective of what you and I find confusing or surprising about the content, we usually have to ask ourselves certain questions: 1)Does the author state his/her...

• Of Mice and Men
Crooks is the only farmhand who is African American. Living as a black man in the Depression Era, and among a bunch of rogue men of their generation, rendered Crooks as an outsider to the group....

• Misery
The ending of "Misery" is not a happy one, but it is realistic. The poor man can't get anybody to listen to his grief. Nobody cares about him. This seems to be the way of the world. If he were a...

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• Hamlet
In Act 1, Scene 1, there is nothing that speaks directly to Hamlet's lack of trust in himself. The scene mostly features the ghost (of Old Hamlet) and how Bernardo, Horatio, and Marcellus react to...

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