Question

shell method bounded by x^2, y=8-7x, x=0

Answer 1

rotated about y-axis?

Answer 2

Yes

Answer 3

Find where y = x^2 and y = 8 - 7x intersect to find the limits of integration.

Answer 4

it looks like 1

Answer 5

\[V = \int\limits_{0}^{1}2\pi x * (8-7x - x^2)dx\]

Answer 6

so just substitute the upper and lower limits?

Answer 7

after moving 2pi out?

Answer 8

Multiply (8-7x-x^2) by x. Then integrate, term by term. Then substitute the upper and lower limits.

Answer 9

I got: 4-(7/3)-(1/4) after multiplying and substituting

Answer 10

Simplify the fractions. Don't forget the 2*pi outside.

Answer 11

2pi*2/3

Answer 12

4/3pi

Answer 13

\( \Large
2\pi (4 - \frac 73 - \frac 14) = 2\pi (\frac {48}{12} - \frac {28}{12} - \frac {3}{12}) = 2\pi (\frac{48-28-3}{12}) = \\ \Large
2\pi (\frac{17}{12}) = \frac{17}{6}\pi
\)

Answer 14

Woah, I was wayy off

Answer 15

Oh, I see where I messed up. The third fraction I put 12, as id I were multipying the whole thing by 12.

Answer 16

Thanks for your help!

Answer 17

You are welcome.