Exam 5: Integration

Approximate ln 7.1 to 3 decimal places.

Evaluate .

Answer true or false.

Answer true or false. .

Answer true or false.

Given f(x) = x³ , [2, 5]. Use the rectangle method to approximate the area using 4 rectangles. (Assume the graph goes through the midpoint of each rectangle.)

Evaluate the integral by making the indicated substitution. , u = 6x² + 7

Evaluate .

Evaluate .

Let f(x) = e^-3x , the simplest exact value of f(ln 4) =

Evaluate .

Express as two integrals with no absolute value.

Simplify. e^{8 ln x} =

Find if .

Evaluate .

For , what is a good choice for u?

Answer true or false.

Estimate the area under the curve by dividing the interval [1, 5] into 4 subintervals of equal length and constructing rectangles over the intervals. (Assume the graph goes through the midpoint of each rectangle.)

Use a simple area formula from geometry to find the area under function A(x) that gives the area between the function f(x) = 4x + 6 and the interval [a, x] = [0, x].

Evaluate .