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

Question

Mathematics

Nehemiah

7 October, 21:09

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

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Carl Sanford · 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€.