Exam 8: Techniques of Integration

The integral $\int \frac { x + 1 } { e ^ { x } } d x$ is

The improper integral $\int _ { 0 } ^ { \infty } x e ^ { - x } d x$ is

The integral $\int \sin ^ { 4 } x \cos ^ { 3 } x d x$ is

The integral $\int \frac { 1 } { x ^ { 2 } + 2 x + 10 } d x$ is

The integral $\int \sqrt { 9 - 16 x ^ { 2 } } d x$ is

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

The improper integral $\int _ { 0 } ^ { \infty } e ^ { - x } d x$ is

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

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

An object in rectilinear motion is moving along a horizontal line with velocity $v ( t ) = \sin ^ { 3 } ( t )$ m/s for the time interval $0 \leq t \leq \frac { 3 \pi } { 4 }$ seconds. What is the net displacement from t = 0 to $t = \frac { 3 \pi } { 4 }$ ?

The integral $\int \frac { x + 1 } { \sqrt { 8 - 2 x - x ^ { 2 } } } d x$ is

The integral $\int \frac { 1 } { \sqrt { 4 x - x ^ { 2 } } } d x$ is

The integral $\int \frac { 1 } { 16 x ^ { 2 } - 25 } d x$ is

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

Using the Trapezoidal Rule with n = 4, the approximated value of $\int _ { 1 } ^ { 2 } \frac { e ^ { x } } { x } d x,$ to three decimal places, is

The integral $\int \frac { 1 } { ( x + 1 ) \left( x ^ { 2 } + 2 x + 10 \right) } d x$ is

The integral $\int \sin x \cos ( 2 x ) d x$ is

Using Simpson's Rule with n = 4, the approximated value of $\int _ { 0 } ^ { 1 } e ^ { x ^ { 2 } } d x,$ to three decimal places, is

The integral $\int \frac { x ^ { 2 } + 1 } { 2 x ^ { 2 } - 5 x } d x$ is

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