Solve 33 no Q 33 Find ∫0π4dxcos3x2 sin 2x - Maths - Integrals

Question

Solve 33 no
Q 33 Find ∫ 0 π 4 d x cos 3 x 2   sin   2 x

Aarushi Mishra · Accepted Answer

I=∫0π41cos3x2 sin 2xdx=∫0π41cos3x2×2 sin x cos xdx=12∫0π41cos3xsin x12 cos x12dx=12∫0π41cos3xsin xcos x12 cos x12×cos x12dx=12∫0π41cos4xtan x12 dx=12∫0π4sec2x sec2xtan x12 dx=12∫0π41+tan2x sec2xtan x12 dxLet tan x=tdt=sec2x dxI=12∫011+t2t12 dt=12∫011t12 dt+12∫01t2t12 dt=12∫01t-12dt+12∫01t32 dt=12×2t1201dt+12×25t5201=1+15=65

Solve 33 no. Q.33. Find ∫ 0 π 4 d x cos 3 x 2 sin 2 x .

Solve 33 no.
Q.33. Find $\int_{0}^{\frac{π}{4}} \frac{d x}{\cos^{3} x \sqrt{2 \sin 2 x}} .$