<p>How do I do these?</p>
<p>Integral of (e^sinx) cosx from 0 to pi/2</p>
<p>Integral of (x^2)/(x^3 - 5) from 0 to pi/3</p>
<p>Integral of 3x-2 so that f(-1) = 2</p>
<p>9-t^2 Find the displacement, when it stopped, moved left, moved right, and the total distance</p>
<p>Integral of sin2xcosx from -pi/2 to pi/6</p>
<p>Area between 16-x^4 and 12-3x^2</p>
<p>I’m not gonna solve it for you, but here are some hints</p>
<p>1) set u = sin x
2) set u = x^3
3) use the initial condition given to find C
4) remember, moving left means 1st derivative is negative, moving right means 1st derivative is positive
5) set u = sin2x, do the chain rule to find the derivative
6) area between two curves is the integral of the difference between the “upper” function and the “lower” function, with limits of integration being their points of intersection</p>
<p>I thought we were not allowed to give homework help on CC?</p>
<p>oh well, it’s not like I gave him answers though</p>
<p>How do I do these?</p>
<p>Integral of (e^sinx) cosx from 0 to pi/2
Using U-Substitution…
u=sinx
du=cosx dx
integral of e^u du from 0 to pi/2
e^sinx evaluated from 0 to pi/2
e^sin(pi/2)-e^sin(0)
e-1</p>
<p>Integral of (x^2)/(x^3 - 5) from 0 to pi/3</p>
<p>Using U-sub again…
u=x^3-5
du=3x^2 dx
1/3*integral of du/u
1/3 ln|x^3-5| evaluated from 0 to pi/3
1/3 ln|-5| - 1/3 ln|[(pi^3)/3] - 5|</p>
<p>Integral of 3x-2 so that f(-1) = 2</p>
<p>integral of 3x-2 dx=3/2x^2-2x+C
Solve for C using f(-1)=2
2=3/2(-1)^2-2(-1)+C
C=-3/2
ANS: 3/2x^2-2x-3/2</p>
<p>9-t^2 Find the displacement, when it stopped, moved left, moved right, and the total distance</p>
<p>Is this a position curve, velocity curve, or acceleration curve? This is needed to solve.</p>
<p>I’m too tired to do the last few, but I hope this was of help to you.</p>
<p>-Pacman</p>
<p>sorry, for #2 i meant u = (x^3)-5</p>
<p>and Pacman10, come on you have to let the guy do it on his own, instead of spoonfeeding him with answers</p>
<p>Actually, for #2, u = x^3 does work, but u = x^3 - 5 makes the ensuing integral in terms of u easier to see the antiderivative.</p>
<p>Go to wolframalpha.com, plug in the equation, hit enter, and then scroll down and it shows you the integral. If you don’t understand how wolframalpha integrated it, you can hit show steps and it will show you all the steps for how it integrated it.</p>
<p>thrill3rnit3- if he is in AP Calc, he is old enough to decide for himself how he is going to learn the material. If he is going to just copy the solution without thinking, then its his decision, and will ultimately hurt him in the end. However, sometimes we need to see the solution for one problem to understand how to do the entire set of problems, in which case asking for the solution to one would be a responsible and smart way to learn material.</p>