Applications of Integration - Integration as an Inverse Process of Differentiation

Applications of Integration - Integration as an Inverse Process of Differentiation

Find \(\frac{\mathrm{d}}{\mathrm{d}x}(\sin x^{2})\).
Hence, find \(\displaystyle\displaystyle \displaystyle\int x^{3}\cos x^{2} dx\).

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Answer:(i) \(2x\cos x^2\) (ii) \(\frac{1}{2}\left(x^2\sin x^2+\cos x^2\right)+C\)

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