Question

The integral \( \int_{-1}^{1} (1 - |x|) \, dx \) is equal to :

• A. \( 2 \int_{0}^{1} (1 + x) \, dx \)
• B. \( 2 \int_{-1}^{0} (1 + x) \, dx \)
• C. \( 0 \)
• D. \( 2 \int_{-1}^{0} (1 - x) \, dx \)

Hint:

For definite integrals with symmetric limits \( [-a, a] \), always evaluate if the function is even or odd. If even, remember that \( \int_{-a}^{a} f(x)dx = 2\int_{-a}^{0} f(x)dx \), and then replace \( |x| \) with \( -x \) since \( x \) is negative in that domain.

Answer 1

The Correct Option is B