## Related questions with answers

Question

The region between the curve $y=1 /(2 \sqrt{x})$ and the x-axis from x = 1/4 to x = 4 is revolved about the x-axis to generate a solid.

Find the volume of the solid.

Solution

VerifiedAnswered 4 months ago

Answered 4 months ago

Step 1

1 of 2Using disk method and vertical strip, the volume is:

$\begin{aligned} V&=\int_a^b \pi [R(x)]^2\: dx \\ &=\pi \int_{1/4}^4 \frac{1}{4x}\: dx \\ &=\frac{\pi}{4}\int_{1/4}^4 \frac{1}{x}\: dx \\ &=\frac{\pi}{4}\left.\ln x\right|_{1/4}^4 \\ &=\frac{\pi}{4}\left(\ln 4-\ln \frac{1}{4}\right) \\ &=\frac{\pi}{4}(\ln 4+\ln 4) \\ &=\frac{\pi}{2}\ln 4 \\ &=\pi \ln 4^{1/2} \\ &=\pi \ln 2 \end{aligned}$

## Create an account to view solutions

By signing up, you accept Quizlet's Terms of Service and Privacy Policy

## Create an account to view solutions

By signing up, you accept Quizlet's Terms of Service and Privacy Policy

## More related questions

1/4

1/7