W01 Stepwise

Due date: Thursday 1/15, 11:59pm

Shells

01

01

Shells volume - offset graph, $y$-axis

Consider the region in the first quadrant bounded by the lines $x=0$, $x=2$, $y=0$, and the curve $y=\frac{1}{\sqrt{x^2+1}}$. Revolve this about the $y$-axis.

Find the volume of the resulting solid.

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Solution

Solutions---0030-01

IBP

02

01

Integration by parts - A and E

Compute the integral:

$$\int (2x+9)e^{x}dx$$

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Solution

Solutions---0010-01

03

02

Integration by parts - A and T

Compute the integral:

$$\int x^2\sin xdx$$

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Solution

Solutions---0010-02