Calculus Answers

Evaluate ∫_1^4▒1/〖(x-3)〗^(1/3) dx

(xy)^x=e, solve for y'

integral of e^(-x^2)

Using polar coordinates, evaluate the integral ∫∫Rsin(x^2+y^2)dA where R is the region 16≤x^2+y^2≤25.

Using polar coordinates, evaluate the integral ∫∫Rsin(x^2+y^2)dA where R is the region 16≤x^2+y^2≤25.

Find the average value of f(x,y)=5 x^2 y^4 over the rectangle R with vertices (−2,0),(−2,6),(2,0),(2,6).
Average value =

I don't know if you're able to see this image at https://webwork.rit.edu/webwork2_files/tmp/MATH-219-02_03_10//gif/4d7caeca-b3b1-3f36-8691-009b499f8636___31f9a87a-cfd8-36da-a364-9b288b49d15b.png. Suppose R is the shaded region in the figure. As an iterated integral in polar coordinates,
∬Rf(x,y)dA=∫(A to B)∫(C to D)f(rcos(θ),rsin(θ))rdrdθ
with limits of integration

A =

B =

C =

D =

Find the volume of the solid bounded by the planes x = 0, y = 0, z = 0, and x + y + z = 6.

Evaluate the double integral I=∫∫D xy dA where D is the triangular region with vertices (0,0),(6,0),(0,1).

Evaluate the integral by reversing the order of integration.
∫(0 t0 3)∫(y^2 to 9) ycos(x^2)dxdy=