Exam 8: Techniques of Integration

The integral $\int \frac { x ^ { 2 } } { \sqrt { 9 x ^ { 2 } + 4 } } d x$ is

Suppose you want to use the Midpoint Rule with n = 4 and equal-length subintervals to approximate $\int _ { 1 } ^ { 6 } e ^ { - x } d x$ ? What is ?x used for this approximation?

The integral $\int \frac { x ^ { 2 } } { x ^ { 2 } - 2 x - 3 } d x$ is

The integral $\int 2 ^ { x } \cos x d x$ is

The integral $\int \frac { x ^ { 2 } + 1 } { x \left( x ^ { 2 } - 4 \right) } d x$ is

The integral $\int \frac { x ^ { 3 } + 3 x - 4 } { x - 2 } d x$ is

The integral $\int x \left( \frac { 1 } { 2 } \right) ^ { x } d x$ is

The improper integral $\int _ { 1 } ^ { \infty } \frac { 1 } { x ^ { 2 } + 1 } d x$ is

The integral $\int x ^ { 3 } \ln x d x$ is

The improper integral $\int _ { 0 } ^ { 1 } \frac { x } { \left( 1 - x ^ { 2 } \right) ^ { \frac { 3 } { 2 } } } d x$ is

The integral $\int \sin ^ { 3 } x \cos ^ { 2 } x d x$ is

The integral $\int \sin ^ { 2 } x \cos ^ { 2 } x d x$ is

Using Simpson's Rule with n = 6, the approximated value of $\int _ { \frac { \pi } { 2 } } ^ { \frac { 3 \pi } { 2 } } \frac { \sin x } { x } d x,$ to three decimal places, is

The improper integral $\int _ { 0 } ^ { \frac { \pi } { 2 } } \frac { 3 x } { \sin ^ { 2 } x } d x$ is

The integral $\int \frac { 1 } { x ^ { 2 } - 2 x - 3 } d x$ is

The integral $\int \frac { 3 x - 6 } { \sqrt { 4 x - x ^ { 2 } } } d x$ is

The integral $\int x \sqrt { 2 x + 3 } d x$ is

The integral $\int \frac { 7 x + 3 } { x ^ { 3 } - 2 x ^ { 2 } - 3 x } d x$ is

The integral $\int \frac { 1 } { \sqrt { \left( 9 x - x ^ { 2 } \right) ^ { 3 } } } d x$ is

The integral $\int \frac { 3 x + 5 } { \sqrt { 3 x + 6 } } d x$ is