Find the length of the curve given by the equation y= intergral from -pi to x of sqrt(cos(t)) dt for x between -pi and pi. I think I know to do this- at least part of it. I am using the fundamental theorem of calculus and the arc length formula, but I don't know how to find the anti derivative of sqrt(cos(t)).

Question

Find the length of the curve given by the equation y= intergral from -pi to x of sqrt(cos(t)) dt for x between -pi and pi.  I think I know to do this- at least part of it.  I am using the fundamental theorem of calculus and the arc length formula, but I don't know how to find the anti derivative of sqrt(cos(t)).

Ms. Sue · Answer

Camryn/Kira/Dean -- please use the same name for your posts.

Steve · Answer

That antiderivative is not expressible in elementary functions. It is an elliptic integral.

Dean · Answer

Ok but then how would I solve this problem?

Steve · Answer

you'd have to use some numeric integration technique to get an approximation.