(a) Find the area of the region enclosed by: $$ y=\sin x \text {, and } y=2 \cos x, \quad \text { over the interval }[0, \pi] $$ (b) Evaluate the following integral: $$ \int \frac{x^{3}}{\sqrt{1-x^{2}}} d x $$

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(a) The area of the region enclosed by the curves $$ y = \sin x $$ and $$ y = 2 \cos x $$ over the interval $$[0, \pi]$$ is $$ 2\sqrt{5} $$. (b) The evaluated integral is $$ -(1-x^2)^{1/2} + \frac{1}{3}(1-x^2)^{3/2} + C $$.

(a) Find the area of the region enclosed by: \[ y=\sin x \text {, and } y=2 \cos x, \quad \text { over the interval }[0, \pi] \] (b) Evaluate the following integral: \[ \int \frac{x^{3}}{\sqrt{1-x^{2}}} d x \]

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(a) Find the area of the region enclosed by: \[ y=\sin x \text {, and } y=2 \cos x, \quad \text { over the interval }[0, \pi] \] (b) Evaluate the following integral: \[ \int \frac{x^{3}}{\sqrt{1-x^{2}}} d x \]

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