Question

First of all, we use the formula of an Area of a Curve.

The formula is \(A = \int_a^b \frac{1}{2} r^2 d\theta\).

You substitute \(r^2 = sin(2\theta)\) or \(r = \sqrt{sin(2\theta)}\) , \(0 \le \theta \le \frac{\pi}{2}\) into \(r\).

You use the double angle trig identity to simplify \(sin 2\theta\) to \(2sin\theta cos\theta\).

Then, you use U-Substitution where \(u = sin \theta\) and \(du = cos \theta\).

You use reverse power rule and you will eventually reach the final answer.

Solutions

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