Exam 5: Integration

Express as a limit.

Answer true or false. If and then

Answer true of false: The average value of f(x) = 5x⁹ on the interval [-5, 5] is 0.

Answer true or false. 5 + 25 + 125 + 625 can be expressed in sigma notation as .

Answer true or false. For $\int$ (1 + sin x)⁶ cos x dx a good choice for u is (1 + sin x)⁶.

Evaluate .

Simplify. ln(e^-4x ) =

Find the area under the curve over the interval [0, 3].

Find g'x) if .

Express in sigma notation with k = 5 as the lower limit.

Answer true or false. is negative.

A particle moves with a velocity of v(t) meters per second along an s-axis. Find the displacement that the particle travels during the period 0 $\le$ t $\le$ 4. v(t) = e ^t + 6.

Estimate the area under the curve by dividing the interval [4, 8] into 4 subintervals of equal length and constructing rectangles over the intervals. (Assume the graph goes through the midpoint of each rectangle.)

Find the area under the curve y = -(x + 7)(x - 5) and above the x-axis.

Answer true or false.

Given f(x) =3x. Use the rectangle method to approximate the area on the range [0, 5] using 4 rectangles. (Assume the graph goes through the midpoint of each rectangle.)

A projectile is launched vertically upward from the ground with an initial velocity of 64 feet per second. When is the projectile 48 feet above the ground?

Evaluate .

Answer true or false. Using the rectangle method to approximate the area under f(x) = 4x⁴ on [0.75, 5.75] with n = 4 yields 8,153. (Assume the graph goes through the midpoint of each rectangle.)

Evaluate .