Let and define

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

Problem

Let f(x)={sin⁡x,x≤π2x−1,x>π2f(x)=\begin{cases}\sin x,& x\le \frac{\pi}{2}\\x-1,& x> \frac{\pi}{2}\end{cases} and define F(x)=∫0xf(t) dtF(x)=\int_{0}^{x} f(t)\,dt. Given that F(0)=0F(0)=0, write an explicit piecewise formula for F(x)F(x) valid for all real xx.

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