The graph of the function is given below. Which of the following definite integrals yields the area of the shaded region?

Question

The graph of the function  is given below. Which of the following definite integrals yields the area of the shaded region?

Quizplus · Accepted Answer

The area of the shaded region can be found by taking the definite integral of the function from x=0 to x=2. The integrand changes at x=1 because the function changes from x^2 to 2-x^2 at that point. Thus, we need to split the integral into two parts:

∫(1)_(0) x^2 dx + ∫(2)_(1) (2-x^2) dx

Evaluating these two integrals gives a total area of 1/3 + 4/3 = 5/3.

The only answer choice that matches this evaluation is B, which is 5/3.

The Graph of the Function Is Given Below