Use a graphing utility to find the area enclosed by the curves y = x⁵, y = -x², x = 0, x = 2. Approximate area to three decimal places. A) 13.333 B) 8.000 C) 8.400 D) 4.400 E) 2.000

Question

Quizplus · Accepted Answer

The area enclosed by the curves y = x^5, y = -x^2, x = 0, and x = 2 can be found by integrating the difference between the two functions (x^5 - (-x^2)) from x = 0 to x = 2. This gives the total area under y = x^5 and above y = -x^2 in that interval. The exact integral is ∫(x^5 + x^2) dx from 0 to 2, which equals [(1/6)x^6 + (1/3)x^3] from 0 to 2 = (1/6)*2^6 + (1/3)*2^3 = 64/6 + 8/3 = 32/3 + 8/3 = 40/3 = 13.333 to three decimal places.

Use a Graphing Utility to Find the Area Enclosed by the Curves