## Q. 13.1

Given  $\frac{\mathrm{d} y}{\mathrm{~d} x}=\cos x-x, \text { find } y .$

## Verified Solution

We need to find a function which, when differentiated, yields $\cos x − x$. Differentiating sin x yields $\cos x$, while differentiating −x²/2 yields −x. Hence,

$y=\int(\cos x-x) \mathrm{d} x=\sin x-\frac{x^2}{2}+c$

where c is the constant of integration. Usually brackets are not used and the integral is written simply as  $\int \cos x-x d x$.