What's the antiderivative of (sin3x)^2 do with upper limit of Pi/2 and lower limit of 0?

1 Answer
Jun 8, 2018

I=int_0^(pi/2)sin^2(3x)dx=pi/4

Explanation:

I assume you mean the integral

I=int_0^(pi/2)sin^2(3x)dx

Remember the trig identity color(blue)(sin^2(a)=1/2-1/2cos(2a))

I=int_0^(pi/2)1/2-1/2cos(6x)dx

color(white)(I)=[1/2x-1/12sin(6x)]_0^(pi/2)

color(white)(I)=(1/2*pi/2-1/12sin(3pi))-(0-1/12sin(0))

color(white)(I)=pi/4