1.
∫1/6 0 (1/(sqrt(1-9x^2))dx
16∫01√1−9x2dx
16∫01√1−9x2 dx=16∫01√1−(3x)2 dxsubstitute: u=3x, du=3 dx,x=0⇒u=3⋅0=0,x=16⇒u=3⋅16=12=12∫01√1−u2du3=1312∫01√1−u2 dusubstitute: u=sin(θ), du=cos(θ)dθ,u=0⇒θ=arcsin(0)=0,u=12⇒θ=arcsin(12)=π6=13π6∫0cos(θ)√1−(sin(θ))2 dθ=13π6∫0cos(θ)cos(θ) dθ=13π6∫0dθ=13[θ]π60=13⋅π6=π18
