Chapter 1. calc_tutorial_15_3_006

1.1 Problem Statement

{2,3,4}
{3,5,7}
{2,4,6,8}
pow($c,2)/2
$b*$d

Evaluate for the specified function f and the box B.

; 1 ≤ x ≤ $a, 0 ≤ y ≤ $b, 0 ≤ z ≤ $c

1.2 Step 1

Question Sequence

Question 1.1

Recall Fubini's Theorem for triple integrals.

The triple integral of a continuous function f(x, y, z) over a box B = [a, b] × [c, d] × [p, q] is equal to the following iterated integral.

Furthermore, the iterated integral may be evaluated in any order.

The function is not continuous only at x = 1Wh3cvJ2xF4=.

Thus in the box B = [1, $a] × [0, $b] × [0, $c], f(x, y, z) bfdtn5PFpMarVC8x2zfiEQ== continuous.

Correct.
Incorrect.

1.3 Step 2

Question Sequence

Question 1.2

Apply Fubini's Theorem.

5LZz9LLrkYsQ4Xzn6iaWgKLBgknnuARuBO5WpqZK2O8=

Correct.
Incorrect.

1.4 Step 3

Question Sequence

Question 1.3

Evaluate the iterated integral for the function f and box B.

.

= 5dWJhLEUU4Y=lnnc1ItEz0kR4=

Correct.
Incorrect.