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 \(r = sin \theta + cos \theta\) , \(0 \le \theta \le \pi\) into \(r\).

Then, you apply the trig identity \(cos^2 \theta + cos^2 \theta = 1\) to replace it with \(1\).

Therefore, you end it with only \(\frac{1}{2} d\theta\).

You take the integral and you get the final answer.

Solutions

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