A student checks whether is an antiderivative of

MATHEMATICS · Single correct · A Level · Mathematics · Integration · Integration

Problem

A student checks whether F(x)=− cos⁡x+2F(x)=-\,\cos x+2 is an antiderivative of f(x)=sin⁡xf(x)=\sin x. Which statement is most accurate? (a) FF is not an antiderivative because the constant +2+2 changes F′(x)F'(x) to sin⁡x+2\sin x+2.‎ (b) FF is not an antiderivative because the derivative of −cos⁡x-\cos x is −sin⁡x-\sin x.‎ (c) FF is an antiderivative because F′(x)=sin⁡xF'(x)=\sin x and the constant +2+2 could be any real number. (d) FF is not an antiderivative because the constant must be arbitrary, not the fixed value +2+2.‎

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