Find the area bounded by two functions $f(x)=(\cos^{-1}|\cos x|)^2$ and $\cos^{-1}|\cos x|$ for the ordinates $|x|=2\pi$

I tried to solve this problem but could not get correct answer.
I drew their graphs.


and i got $-\pi^2+2\pi$ but the correct answer is $\frac{\pi^3+\pi+8}{6}$

where have i done wrong?Please guide me.


Do you mean the area between the curves? If so, then, by studying the graph (or thinking a bit)


it seems that one should calculate in total $$ 8\biggl[\int_0^1 x-x^2\,dx+\int_1^{\pi/2} x^2-x\,dx\biggr]. $$ Doing so, I end up with $$ \frac{\pi^3}{24}-\frac{\pi^2}{8}+\frac{1}{3}. $$ But I have probably misunderstood something?


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.