Question

The value of the integral \( \int_{-3}^{5} |x - 3| \, dx \) is

• A. 20
• B. 21
• C. 18
• D. 22

Hint:

For integrals involving absolute value functions, break the integral at the points where the function inside the absolute value equals zero.

Answer 1

The Correct Option is A

We split the integral at \( x = 3 \) as the absolute value function has a break point at \( x = 3 \): \[ \int_{-3}^{5} |x - 3| \, dx = \int_{-3}^{3} -(x - 3) \, dx + \int_{3}^{5} (x - 3) \, dx \] Evaluating each integral: \[ \int_{-3}^{3} -(x - 3) \, dx = \int_{-3}^{3} (-x + 3) \, dx = 9 \] \[ \int_{3}^{5} (x - 3) \, dx = \int_{3}^{5} (x - 3) \, dx = 11 \] So, the total value of the integral is: \[ 9 + 11 = 20 \]