Monday

April 21, 2014

April 21, 2014

Posted by **Dylan** on Monday, November 28, 2011 at 5:08pm.

Let R be the region between the graph of f and the x-axis on the interval 0 to 1 . Find the volume V of the solid of revolution generated by revolving R about the x-axis. Give both exact (symbolic) and approximate (numeric) answers.

- calculus -
**MathMate**, Monday, November 28, 2011 at 6:21pmConsider a thin vertical slice of width dx.

If we rotate the slice about the x-axis, we get a disk of thinkness dx and area πf(x)^2, so the volume is

πf(x)^2 dx.

Integrate all slices from 0 to 1 gives you

∫πf(x)^2 dx

Hint: I get 0.995... as the volume, and the symbolic answer has a factor of π/3.

If further assistance is required, feel free to post.

**Related Questions**

calculus - use limit process. find area of region between graph y= -3x + 20 and ...

calculus - let f be the function f(x) = x^3 + 3x^2 - x + 2 a. the tangent to the...

MATH Calculus Homework - Let R be the region between the graph of y=x3 and the x...

Calculus - Use the limit process to find the area of the region between the ...

calculus - Consider the region above the graph of y=x^2 and below the graph of y...

calculus - Consider the region above the graph of y=x^2 and below the graph of y...

Calculus please help!!! double integral - Combine the following two integrals ...

calculus - Find the volume of the solid obtained by rotating the region under ...

calculus - Find the area of the region between the parabola 4y = x^2 and the ...

calculus - Use the limit process to find the area of the region between the ...