Can anyone help me integrate this integral? I'm stumped. $$\int^y_0\dfrac{1}{\sqrt{x(y-x)}}dx$$
Asked
Active
Viewed 37 times
1
-
Hint: $x(y-x)=\frac{1}{4}y^2-(x-\frac{1}{2}y)^2$. Now make a trigonometric substitution. – David May 08 '14 at 03:54
1 Answers
3
Hint: Let $x=y\sin^2\theta$. The integral will collapse.
André Nicolas
- 507,029
-
-
1We are integrating by substitution. If you prefer, we are letting $\theta=\arcsin(\sqrt{x/y})$. – André Nicolas May 08 '14 at 04:11
-
-