How do you integrate intsqrt(1-4x^2) by trigonometric substitution?

1 Answer
Oct 10, 2016

sin^2(theta)/2+c

Explanation:

As shown in the picture below our equation matches the "sin" trigonometric substitution.
enter image source here

Therefor,

x=sin(theta)/2

sqrt(1-4x^2)=cos(theta)

dx=(2cos(theta))/4 d theta=cos(theta)/4

intcos(theta)(cos(theta))/2=1/2intcos^2(theta)d theta

1/2sin^2(theta)+c or sin^2(theta)/2+c

Good Luck!!!