The functions and are antiderivatives of on

MATHEMATICS · Subjective · A Level · Mathematics · Integration · Integration

Problem

The functions P(x)=−cos⁡x+2P(x)=-\cos x+2 and Q(x)=1−cos⁡x−4Q(x)=1-\cos x-4 are antiderivatives of sin⁡x\sin x on R\mathbb R. Find the constant kk such that Q(x)=P(x)+kQ(x)=P(x)+k for all real xx.

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