 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2012/paper-2/2/solution

The chain rule identifies an antiderivative directly:

\frac{d}{d x} e^{s i n (x^{2})} = 2 x cos (x^{2}) e^{s i n (x^{2})} .

The upper limit in the PDF is

π /2

\frac{1}{2} [e^{s i n (x^{2})}]_{0}^{π /2} = \frac{e - 1}{2} .

 New to topics? Read the docs here!