Exam 5: Integration

Find the area of the region between y = 4 -x² and the x-axis.

Find y(x) if and y(0) = 3 .

Given . Use the rectangle method to approximate the area on the range [0, 4] using 4 rectangles. (Assume the graph goes through the midpoint of each rectangle.)

Find the area under the curve f(x) = e^2x over the interval [0, 3].

Answer true or false.

Find the average value of for -1 $\le$ x $\le$ 2.

Answer true or false. 1 + 4 + 9 + 16 can be expressed in sigma notation as .

Evaluate

Find the average value of over the interval [1, 2]. Approximate value to three decimal places.

Find the derivative. .

Evaluate .

Given f(x) = 5x - 3 , [2.5, 7.5]. Use the rectangle method to approximate the area using 4 rectangles. (Assume the graph goes through the midpoint of each rectangle.)

Find the area under the curve over the interval [0, 4].

Approximate ln 4 to 3 decimal places.

A playful student drops your math book from a dormitory window and it hits the ground in 6 seconds. How high up is the window?

Use a simple area formula from geometry to find the area under function A(x) that gives the area under the function f(x) = 8 on the interval [a, x] = [2, x].

Evaluate .

Answer true or false.

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 + 2 on the interval [a, x] = [0, x].

Use a simple area formula from geometry to find the area under function A(x) that gives the area between the function f(x) = 3x -4 and the interval [a, x] = [-2, x].