anyone good with calculus 2 - integration by parts?

Question

need help w/ integrals. i will use "S" for the integral symbol.

sq = square root (e.g. sq.x = square root x)

1. Scos(pi)x (i know this is an easy problem, but the pi is throwing me off)

2. S(sq.x)lnxdx

3. Sxcos(pi)xdx

4. find volume generated by revolving region under graph about y-axis

f(x) = xsinx , x E [0, pi]

5. also, can anyone explain why multiplying (1/x) by (x^n+1) equals x^n?

thanks for any help you can provide

Answer 1

1.
cos (pi) = 1
Scos(pi)x dx = S x dx = x^2 / 2 + c

5. 1/x is the same as x^-1
when you multiply them you add the exponents n+1-1 = n
or you can just look at it as dividing by x^1. when dividing you subtract exponents.

I don't have the energy to do integration by parts right now.

Answer 2

-4 is a relentless distinctive; go away it on my own for now, yet do no longer forget approximately it. a million/(a million+x^2) dx could be built-in rather, so because it is your dv. Arctan(x) could be differentiated rather, so because it is u. a million/(a million+x^2) dx is actual the derivative of arctan x, and arctan x is the required of a million/(a million+x^2) dx, so they are additionally your v and du words. lower back, do no longer forget on the subject of the -4 (you could positioned it with the two one; i bypass to place it with u): u = -4arctan(x) dv = a million/(a million+x^2) dx du = -4/(a million+x^2) dx v = arctan(x) necessary of u dv = (uv - necessary of v du). necessary of [-4arctan(x) * a million/(a million+x^2)] dx = [-4arctan(x) * arctan(x)] - necessary of [arctan(x) * -4/(a million+x^2)] dx + C Does something cancel out on the two aspects? sure; the unique necessary does (however the -4 isn't in the comparable place, it multiplies to the comparable concern). in case you divide the two aspects by using necessary of [-4arctan(x) * a million/(a million+x^2)] dx, you're left with a million = [-4arctan(x) * arctan(x)] + C, bypass from there.

Answer 3

5. (1/x)*(x^n+1) = (x^n+1)/x = [x(x^n)]/x = x^n

Answer 4

Check out this website...it's great.

http://integrals.wolfram.com/index.jsp

It'll help you with the first three, anyway.