calc_tutorial_15_1_040

Problem Statement

{3,5,7}

{2,4,6}

pow(4,2)/2

{1}

7+1

Evaluate the integral.

Step 1

Question Sequence

Question 1

Recall Fubini's Theorem. The double integral of a continuous function f(x, y) over a rectangle R = [a, b] × [c, d] is equal to the iterated integral (in either order):

The function is not continuous only at x = .

Thus in the rectangle R = [0, 7] × [0, 4], f(x, y) continuous.

Correct.

Incorrect.

Step 2

Question Sequence

Question 2

Apply Fubini's Theorem. We will chose to use the order of x first.

Where d = and b = .

Correct.

Incorrect.

Step 3

Question Sequence

Question 3

Since the integrand can be written as the product of two functions f(x, y) = h(y)g(x), the double integral is the product of two single integrals.

Evaluate .

Correct.

Incorrect.

Step 4

Question Sequence

Question 4

Evaluate .

= ln

Correct.

Incorrect.