 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2013/paper-1/10/b/solution

Subtract the lower curve from the upper curve on the intersection interval. The definite integral is

A = \int_{- 1}^{1} [(1 - x^{4}) - (x^{2} - 1)] d x = 2 \int_{0}^{1} (2 - x^{2} - x^{4}) d x = \frac{44}{15} .

The result is in square coordinate units.

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