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MathRefer the graph in the attached image. From the graph, Area of the region that lies beneath the curve `~~` 6/100(Area of Rectangle) Area of the region `~~` 6/100(5*1) `~~` 0.30 Exact Area of the...

MathRefer the graph in the attached image. From the graph it appears that the area is `~~` 2/3 of the rectangle. Area of the region= `~~` 2/3(Area of rectangle) Area of the region...

MathYou 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`...

MathEvaluate `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

Math`int_0^1(u+2)(u3)du` `=int_0^1(u^23u+2u6)du` `=int_0^1(u^2u6)du` `=[u^3/3u^2/26u]_0^1` `=[1^3/31^2/26*1][0^3/30^2/26*0]` `=(1/31/26)` `=(2336)/6` =37/6

MathEvaluate `int_0^4(4t)(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 function...

MathHello! Find the indefinite integral first: `int((x1)/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...

Math`int_0^2 (y1)(2y+1)dy` Before evaluating, expand the integrand. `=int_0^2 (2y^2+y2y1)dy` `=int_0^2(2y^2y1)dy` Then, apply the integral formulas `int x^n dx=x^(n+1)/(n+1)` and `int cdx = cx` ....

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)` Plugin the...

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)...

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]`...

Math`int_1^4(52t+3t^2)dt` apply the sum rule and power rule, `=[5t2t^2/2+3t^3/3]_1^4` `=[5tt^2+t^3]_1^4` `=[5*44^2+4^3][5*11^2+1^3]` `=(2016+64)(51+1)` `=(8416)(5)` =63

Math`int_0^1(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))]_0^1` `=[u+u^5/10u^10/25]_0^1 = [1+1^5/101^10/25][0+0^5/100^10/25]` `=(1+1/101/25)` `=(50+52)/50` =53/50

MathYou 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)(271)` `int_1^9 sqrt x dx...

MathEvaluate `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[21]` =3

MathHello! 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).`...

Math`F(x)=int_x^pisqrt(1+sec(t))dt` `F(x)=int_pi^xsqrt(1+sec(t))dt` `F'(x)=d/dxint_pi^xsqrt(1+sec(t))dt` `F'(x)=sqrt(1+sec(x))`

MathYou need to use the Part 1 of the FTC to evaluate the derivative of the function. You need to notice that the function G(x) is the composite of two functions `f(x) = int_1^x cos t dt ` and `g(x) =...

MathHello! 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...

MathHello! 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))`...

MathYou need to use the Part 1 of the FTC to evaluate the derivative of the function. You need to notice that the function y is the composite of two functions `f(x) = int_1^x sqrt(1+sqrt t) dt` and...

MathHello! 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...

Math`y=int_(13x)^1(u^3/(1+u^2))du` Let t=13x `dt/dx=3` `dy/dx=dy/dt*dt/dx` `y'=d/dxint_(13x)^1(u^3/(1+u^2))du` `=d/dtint_t^1(u^3/(1+u^2))du.dt/dx` `=d/dtint_1^t(u^3/(1+u^2))du.dt/dx`...

Math`y = int_1^(sin (x)) (sqrt(1 + t^2))dt` Use Part 1 of the Fundamental Theorem of Calculus to find...You need to use the Part 1 of the FTC to evaluate the derivative of the function. You need to notice that the function h(x) = y is the composite of two functions `f(x) = int_1^x sqrt(1+t^2)dt` and...

MathYou 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...

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, plugin the limits of the integral as follows `F(x) =int_a^bf(x) dx = F(b)...

MathHello! 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...

MathHello! 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^2t)` and `g(x)=F_3(x).` Therefore...

MathHello! 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)=(tt^2)^8` and `g(x)=F_5(x).` Therefore...

HistoryThere 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...

Aristotle<strong>Feedback and rewards</strong> Aristotle was a Greek philosopher. He was mentored by Plato and went on to become the mentor and tutor of Alexander the Great. His philosophical...

PoliticsThe 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...

Social SciencesCompatibilism 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...

HistoryLincoln'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...

HistoryColumbus's motivation for his voyage was to reach Asia by sailing west. Neither he nor his backers (nor the people who thought his voyage illadvised) knew that he would reach the "New World" by...

MacbethIn Act 2, Scene 2, Macbeth meets Lady Macbeth having just "done the deed" (killed Duncan and his guards). Both Macbeth and Lady Macbeth are very much on edge. Lady Macbeth's confidence is shaken...

ReferenceSpace exploration's values divide into two categories: human curiosity, and free enterprise (capitalism). The first category holds scientific inquiry  how does the universe work? What are the...

HealthTo 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...

1984One of the ideas prevalent in 1984 is the idea of the government controlling the people. When Winston is talking to Julia about the war, she expresses the opinion that it is not real. “The...

Of Mice and MenCrooks 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....

A Midsummer Night's DreamTheseus first sides with Egeus and tells Hermia to obey him, and then changes his mind and overrules Egeus to tell her she can marry Lysander. Theseus either contradicts himself or changes his mind...

MiseryThe 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...

HistoryWorld War II was fought for many reasons, stretching back to the end of World War I. But the main cause of World War II was the rise of dictatorships in the 1930s. There were dictators in many...

Of Mice and MenCandy’s dog is old and smelly, and for this reason Carlson shoots it. Candy is the old swamper, and he has a very old dog. The dog is considered too old and smelly, and Carlson offers to shoot...

HamletIn 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...

MacbethFleance escapes because the witches pronounce that Banquo’s sons will be king. Aside from the purposes of historical accuracy, Fleance needs to escape so that all three of the witches' original...

HistoryThis phrase is found in the opening passage of the Declaration, where Jefferson is explaining why a declaration is needed in the first place. In this context "station" means something like "status"...

Thank You, M'amIn Thank You, M'am by Langston Hughes, the reader is immediately introduced to Mrs. Luella Bates Washington Jones and can form an opinion of her quite readily. The fact that her purse contains a...

ScienceThe term "mRNA" stands for "messenger RNA." This is usually enough of a hint to remember their function; to carry messages in the body, specifically messages for creating proteins. The mRNA is like...

Stopping by Woods on a Snowy Evening‘Stopping by woods’ may appear to be a simple and small poem, yet one can unravel deeper and serious themes running through it. The beauty of the woods is so fascinating that the traveler...