Question

Evaluate the integral the square root of: (2-x^2) dx by substituting x=the square root of: (2) sintheta.

Answer 1

\[\int\limits_{a}^{b}\sqrt{2-x ^{2}}d(theta)\]

\[\int\limits_{a}^{b}\sqrt{2-2sin ^2\theta}d \theta\]

\[\int\limits_{a}^{b}\sqrt{2(1-\sin^2)\theta}d \theta\]

\[\int\limits_{a}^{b}\sqrt{2\cos^2\theta}d \theta\]

\[\int\limits_{a}^{b}\sqrt{2}\cos thetad \theta\]

\[\sqrt{2}\sin \theta + C\]