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## Educators

Rk
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### Problem 1

Let $S$ be the solid obtained by rotating the region shown in the figure about the y-axis. Explain why it is awkward to use slicing to find the volume $V$ of $S$. Sketch a typical approximating shell. What are its circumference and height? Use shells to find $V$.

Amrita B.

### Problem 2

Let $S$ be the solid obtained by rotating the region shown in the figure about the y-axis. Sketch a typical cylindrical shell and find its circumference and height. Use shells to find the volume of $S$. Do you think this method is preferable to slicing? Explain.

Amrita B.

### Problem 3

Use the method of cylindrical shells to find the volume generated by rotating the region bounded by the given curves about the y-axis.

$y = \sqrt[3]{x}$ , $y = 0$ , $x = 1$

Amrita B.

### Problem 4

Use the method of cylindrical shells to find the volume generated by rotating the region bounded by the given curves about the y-axis.

$y = x^3$ , $y = 0$ , $x = 1$ , $x = 2$

Amrita B.

### Problem 5

Use the method of cylindrical shells to find the volume generated by rotating the region bounded by the given curves about the y-axis.

$y = e^{-x^2}$ , $y = 0$ , $x = 0$ , $x = 1$

Leon D.

### Problem 6

Use the method of cylindrical shells to find the volume generated by rotating the region bounded by the given curves about the y-axis.

$y = 4x - x^2$ , $y = x$

Amrita B.

### Problem 7

Use the method of cylindrical shells to find the volume generated by rotating the region bounded by the given curves about the y-axis.

$y = x^2$ , $y = 6x - 2x^2$

Amrita B.