Which of the following definite integrals could be used to calculate the total area bounded by the graph of y = 1 - x^2 and the x-axis?

Question

A)

B)

C)

D)

Answer 1

The answer is D. The x interval where 1 - x^2 >= 0 is [-1, 1], so the natural integral for the area would be the integral from -1 to 1 of the function. However, since the function is symmetric about 0, the integral from -1 to 0 equals the integral from 0 to 1, so the integral from -1 to 1 equals twice the integral from 0 to 1.