1. Find the volume of the solid generated by revolving region bounded by: y=x 2

Question

1. Find the volume of the solid generated by revolving region bounded by: y=x2, y=4x-x2 graphs about of the y=6.

my total volume answer was pi* (36x2/2 + 17x^3/3 + 2x^4 + x^5/5) from (0 to 2) but I am not getting the correct number value.

2. Find the volume generated by revolving the region bounded by: y=6-2x-x2, y=x+6. graphs about of the x=1.

my answer for total volume was 2pi* (x^4/4 + 2x^3/3 - 3x2/2) from (-3- to 0) but again my the number

3. Evaluate the integral: 4sin(x)-4cos(2x)

my answer for this was 2sin(pi/3)+4cos(pi/6).. but that's wrong

4. Find the area S of the region: y=3sin(x), y=e^3x. x=0, x=pi/2

my answer was: 1/3e^(3pi/2)-3cos(pi/2) that's wrong as well..

5. Find the volume: x=3y^2 x=3 about x=3

my answer was 78pi/15

You do not have to answer all of them, i'll award points to the best answer. I've been working on these homework problems for the past couple days and these are the 5 that i've gone through countless pieces of paper trying to figure out. Thank you.

Explanation / Answer

int from 0 t0 pi/2 {4sin(x)-4 cos(2x)}dx=[-4cosx-2sin(2x) ]0pi/2 =4

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