A student writes the following to show that : “Since

MATHEMATICS · Subjective · CBSE · Mathematics · Integrals · Integrals

Problem

A student writes the following to show that ∫sin⁡x dx=−cos⁡x+C\displaystyle \int \sin x\,dx= -\cos x+C: “Since ddx(cos⁡x)=sin⁡x\dfrac{d}{dx}(\cos x)=\sin x, the antiderivative of sin⁡x\sin x is cos⁡x+C\cos x+C.” (i) Identify and explain the error in this reasoning. (ii) Give the correct verification that −cos⁡x-\cos x is an antiderivative of sin⁡x\sin x.

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