Chapter 1. calc_tutorial_15_1_040

1.1 Problem Statement

{3,5,7}

{2,4,6}

pow($b,2)/2

{1}

$a+$e

Evaluate the integral.

1.2 Step 1

Question Sequence

Question 1.1

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 = 8SMCMW9N2Ew=.

Thus in the rectangle R = [0, $a] × [0, $b], f(x, y) bfdtn5PFpMarVC8x2zfiEQ== continuous.

Correct.

Incorrect.

1.3 Step 2

Question Sequence

Question 1.2

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

Where d = iSba6t70dtA= and b = nc1ItEz0kR4=.

Correct.

Incorrect.

1.4 Step 3

Question Sequence

Question 1.3

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 .

= SFgqQUkJGdg=

Evaluate .

= irsMJ3dL950=

Correct.

Incorrect.

1.5 Step 4

Question Sequence

Question 1.4

Evaluate .

= SFgqQUkJGdg=lnU2GIbglD1oM=

Correct.

Incorrect.