## Practice Problems for Module 2

### Exercises

**Directions:** You should try to solve each problem first, and then click "Reveal Answer" to check your answer.
You can click "Watch Video" if you need help with a problem.

1. The base of a solid is the region enclosed by \(x = y^2 − 9\) and \(x = 7\). Its cross-sections are perpendicular to the \(x\)-axis and are equilateral triangles. Set up an integral to find the volume of the solid.

2. The base of a solid is the region enclosed by \(y = \sqrt{x + 5}\), \(x = 4\) and the \(x\)-axis. Its cross-sections are perpendicular to the \(y\)-axis and are semicircles. Set up an integral to find the volume of the solid.

3. Set up an integral representing the volume of the solid obtained by rotating the region bounded by the following curves about the \(x\)-axis: \(y =\dfrac{2}{x}\), the \(x\)-axis, \(x = 1\) and \(x = 4.\)

4. Set up an integral representing the volume of the solid obtained by rotating the region bounded by the following curves about the line \(x=7\): \(x=y^2 +3\) and \(x=7.\)

5. Set up an integral representing the volume of the solid obtained by rotating the region bounded by the following curves about the \(y\)-axis: \(y = \ln(x)\), the \(x\)-axis and \(x = e.\)

6. Set up an integral representing the volume of the solid obtained by rotating the region bounded by the following curves about the line \(y=5\): \(y = \sqrt{x+1}\), the \(x\)-axis and \(x = 8.\)