Question 15.4.19

Suppose we want to find $\int x \cos x \dif x$, so we’re looking to find a function that has the derivative $x\cos x$. Any ideas?

  1. Our first thought might be ‘$\frac{\dif}{\dif x} \sin x = \cos x$ so maybe something like $x\sin x$ might work.’ See if that works, and if it doesn’t then modify it so that it does. Show assumed knowledge

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  2. What about a definite integral? Find $\int_0^{\pi/2} x\cos x\dif x$ Show answer