Exam 5: Integration

Use a simple area formula from geometry to find the area under function A(x) that gives the area between the function f(x) = 7 and the interval [a, x] = [6, x].

Evaluate .

Answer true or false. The area between y = x⁷ + cos x and the x-axis on [0, 5] is .

Express the antiderivative of on the interval (- $\infty$ ,+ $\infty$ ) as an integral, F(x), whose value at x = -3 is 0.

Find the position at time t = 3 second of a particle if v(t) = 4t - 6; s = 8 when t = 0.

Answer true or false.

Given f(x) = 7 + x . Use the rectangle method to approximate the area on the interval [0, 3] using 4 rectangles. (Assume the graph goes through the midpoint of each rectangle.)

Find y(x) if and y(0) = 1.

Find the average value of f(x) = (x + 1)² over [-1, 2]. Approximate value to three decimal places.

Find the displacement of a particle if v(t) = t⁴ + 4; [0, 5].

Evaluate .

Answer true or false. .

Find the average value of for .

Evaluate .

Simplify. ln(e ^{- 7x} ) =

A projectile fired upward from the ground is to reach 144 feet. What must be its initial velocity?

Evaluate

Evaluate the integral by making the indicated substitution. , u = x⁴ .

A particle is moving so that its velocity, v(t) = t² -3t - 10 for 0 $\le$ t $\le$ 7. Find the total distance travelled by the particle.

Evaluate if .