Exam 5: Integration

Evaluate .

Find the displacement of a particle if v(t) = t³ + 2; [0, 4].

Evaluate

Find the average value of f(x) = x² over the interval [-1, 1].

Answer true or false.

Find the area under the curve y = -(x + 6)(x - 4) and above the x-axis.

Evaluate .

Evaluate .

Evaluate .

Let f(x) = e ^{- 4x} , the simplest exact value of f(ln 2) =

Use a simple area formula from geometry to find the area under function A(x) that gives the area under the function f(x) = 5x - 5 on the interval [a, x] = [-1, x].

Find the area enclosed by , , x = 2, and x = 3.

Evaluate .

Evaluate the integral by making the indicated substitution. , u = 1 + x

Find if .

Find the area under the curve y = x² - 4 on [1, 3].

Find the position at time t = 3 second of a particle if v(t) = 2t - 8; s = 7 when t = 0.

Express in sigma notation, but do not evaluate. 9 + 16 + 25 + 36 + 49 + 64 + 81

Find F ''(x) if .

Evaluate .