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(a) $$2 \pi\left[b^{2}+\frac{a^{2} b \sin ^{-1} \frac{\sqrt{a^{2}-b^{2}}}{a}}{\sqrt{a^{2}-b^{2}}}\right]$$

(b) $$2 \pi a^{2}+\frac{2 \pi a b^{2}}{\sqrt{a^{2}-b^{2}}} \ln \frac{\sqrt{a^{2}-b^{2}}+a}{b}$$

a) $$

2 \pi\left[\frac{a^{2} b}{\sqrt{a^{2}-b^{2}}} \arcsin \left(\frac{\sqrt{a^{2}-b^{2}}}{a}\right)+b^{2}\right]

$$

b) $$

2 \pi a^{2}+\frac{2 \pi a b^{2}}{\sqrt{a^{2}-b^{2}}} \ln \left(\frac{a+\sqrt{a^{2}-b^{2}}}{b}\right)

$$

Applications of Integration

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