# Integral with square root

• December 1st 2007, 05:03 PM
liyi
Integral with square root
Evaluate $\int_{-8}^8\sqrt{64-x^2}\,dx$
• December 1st 2007, 05:22 PM
Jhevon
Quote:

Originally Posted by liyi
Evaluate $\int_{-8}^8\sqrt{64-x^2}\,dx$

the easy way: you could realize that this integral gives you the area of the upper half of the circle with radius 8

the hard way: use the trig substitution $x = 8 \sin \theta$ ....since we have an even function here, you may also wish to change the problem to $2 \int_0^8 \sqrt{64 - x^2}~dx$, and change the limits based on the trig substitution