Use cylindrical shells to compute the volume of a napkin ring of height 3h created by drilling a hole with radius r through the center of a sphere of radius R and express the answer in terms of h...

Sketch the region in the xy-plane defined by the inequalities
x − 3y2 ≥ 0, 2 − x − 5|y| ≥ 0
and find its area.
If I did it correctly, I have a region defined by x=3y^2, (x-2)/5, -(x-2)/5...

Integral from 0-t of e^-x/(1+(e^-x)) dx
I let u = e^-x and du=-e^-x dx. Then it is -1 times the integral of 1/ (1+u) du from 1 to e^-t
which equals -(ln(1+u) from 1to e^-t
which...

I need to integrate from 0-t. I am told to set u= Erf and u'= (2e^-x^2)/pi^1/2. v' is 1 and v=x.
i am also told that the answer is t Erf(t)+ ((e^-t^2)-1)/pi^1/2
how many...

Calculate an expression for the int from 1 to e of (ln(x))^k dx in terms of the integral from 1 to e of (ln(x))^k-1 dx.
essentially, I need to integrate by parts to get this equality:
The...