Exam 5: Integration

Evaluate .

Set up the integral to find the area between and the x-axis on [-5, -3] .

Answer true or false.

Write the expression in sigma notation. 2 - 4 + 6 - 8 + 10 - 12 + 14.

Find the average value of for .

Evaluate .

Answer true or false. $\int$ cos ⁵x dx can be easily solved by letting u = cos x.

Use a simple area formula from geometry to find the area under function A(x) that gives the area under the function f(x) = 4x + 6 on the interval [a, x] = [-2, x].

Find the average value of f(x) = (x + 1)⁴ over [-1, 5] and find a point x* in [-1, 5] such that .

Answer true or false.

Express 1 + 8 + 64 + 512 + 4,096 + 32,768 in sigma notation with k = 3 as the lower limit.

Express in sigma notation.

Evaluate .

Find the average value of f(x) = 5x + 5 over [0, 4].

Evaluate .

Express as a sum multiplied by a constant.

Write the expression in sigma notation. 7 + 7x + 7x² + 7x³ + 7x⁴.

Find the average value of over the interval [1, 3]. Approximate value to three decimal places.

Given f(x) = 5x- 7 , [2, 5]. Use the rectangle method to approximate the area using 4 rectangles. (Assume the graph goes through the midpoint of each rectangle.)

Express in sigma notation, but do not evaluate. 3 + 4 + 5 + 6