Exam 5: Integration

Evaluate .

Approximate ln 3/2 to 3 decimal places.

Approximate ln 3 to 3 decimal places.

Evaluate .

Find the area under the curve f(x) = e^4x over the interval [0, 5].

Answer true or false. The area between y = x⁴ -x³ and the x-axis on [2, 5] is .

Given f(x) = 4x⁵ , [3, 6]. Use the rectangle method to approximate the area using 4 rectangles. (Assume the graph goes through the midpoint of each rectangle.)

Evaluate .

Answer true or false. .

For $\int$ 7x⁶(x⁷ + 12)⁴ dx what is a good choice for u?

Evaluate if .

Find all values of x* in the interval [0, 6] that satisfy the Mean-Value Theorem for Integrals, where f(x) = x - 6.

Evaluate .

Evaluate .

Find the area between the curve and the x-axis on the given interval. y = x² - 9; [-5, 0]

Find the average value of f(x) = x cos x² for .

Evaluate .

Use a simple area formula from geometry to find the area under function A(x) that gives the area between the function f(x) = x + 7 and the interval [a, x] = [-5, x].

Simplify e^-ln(x+2).

Express in sigma notation with k = 4 as the lower limit.