Exam 8: Techniques of Integration

The integral $\int \log _ { 2 } x d x$ is

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

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

The improper integral $\int _ { 0 } ^ { 4 } \frac { 1 } { ( 4 - x ) ^ { \frac { 3 } { 2 } } } d x$ is

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

The integral $\int \tan x \sec x d x$ is

The integral $\int \frac { x - 3 } { x ^ { 2 } - 6 x + 10 } d x$ is

The improper integral $\int _ { 0 } ^ { 1 } x \ln x d x$ is

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

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

The integral $\int \sec ^ { 4 } x d x$ is

The integral $\int x \sqrt { 4 x + 5 } d x$ is

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

Using the Trapezoidal Rule with n = 4, the approximated value of $\int _ { \frac { 3 \pi } { 2 } } ^ { 2 \pi } \frac { \cos x } { x } d x,$ to three decimal places, is

The integral $\int \frac { 3 - x } { x ^ { 2 } - 6 x + 10 } d x$ is

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

In a newly made preserve in a zoo, 400 rabbits were released. The monthly maximum population growth rate is 8%. Population ecologists have determined that the forest preserve can sustain a population of 6,000 rabbits, and the population will follow a logistic growth model. Which of the following is a logistic differential equation that models the rabbit population, R(t)?

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

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

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