help with this math problem plz?

Question

Let R be the region enclosed by the X axis, the Y axis, the line x = 2, and the curve y =2e^x + 3x.

(a)Find the area of R by setting up and evaluating a definite integral. Your work must include an antiderivative.

(b)Find the volume of the solid generated by revolving R about the Y axis by setting up and evaluating a definite integral. Your work must include an antiderivative.

Answer 1

(a)
We're integrating a solid where x goes from 0 to 2, and at each x, the height of the solid is 2e^x + 3x - 0

Thus the integral to evaluate is:
integral(2e^x + 3x) from 0 to 2

(b)
Since the function is in terms of x and the axis of revolution is y (not the same), use the shell method, which is adding up the area of very thin cylinders. Each cylinder gives us a surface area of 2*pi*r*h.
r is the distance from the y axis. This is always x.
h is the height of the cylinder. This is given by our function, 2e^x + 3x

So the integral this time is:
integral(2*pi*x*(2e^x + 3x)) from 0 to 2

See if you can do each of these integrals.
(Hint: Multiply out the second one, integrate the x*e^x term with integration by parts)

Answer 2

Sorry, but Math is not my strenght. Good luck.

Answer 3

wooohhhhh.....

i think i'll quit taking engineering......