An insect is moving along the curve $r=|cos\theta|$ such that $\theta =\frac{\pi t}{6}$, where $t$ is time measured in seconds. What is the distance travelled by the insect in the time interval between $t=1$ and $t=2$ ?

My attempt: The arc length is given by the formula : $\int_{a}^{b} \sqrt{1+f'(x)^2}$. So here in the given region, we have $r=|\cos\theta|=cos\theta$. Now, we have $\int_{\frac{\pi}{6}}^{\frac{\pi}{3}}\sqrt{1+sin^2(x)}$. This integration is difficult to carry out. I am unable to proceed further.

Any help is appreciated. Thanks in advance.


Recall that the formula for the length of the arc in polar coordinates is:


Replacing we have that:



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.