Question

Evaluate the integral by interpreting it in terms of areas. 0 4 + 36 − x2 dx −6

Answer 1

Answer: Split up the integral. â«(-6 to 0) [2 + sqrt(36 - x^2)] dx = â«(-6 to 0) 2 dx + â«(-6 to 0) sqrt(36 - x^2) dx. The first integral represents the area of a rectangle with base length 6 and height 2. ==> â«(-6 to 0) 2 dx = 6 * 2 = 12. The second integral you figured correctly to be (1/4) Ď€ * 6^2 = 9Ď€. So, the final answer is 12 + 9Ď€.