Question

\text { (a) Let } f(x)=\frac{\cos \left(\pi x^{-2}\right)}{x^{3}} . \text { Compute the average value of } f \text { on the interval }[1, \sqrt{2}] \text {. } (b) Evaluate

the following integral by making the substitution u = x² and then interpreting the result as an area: \int_{0}^{1} x \sqrt{2 x^{2}-x^{4}} d x

Fig: 1

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