Question

∫ 0 π/4 ​ sin 2 x cos 2 xdx​

Answer 1

Step-by-step explanation:

π/4

cos

2

5

x

sin

2

1

x

dx

=∫

0

π/4

cos

2

x

tan

2

1

x

dx

=∫

0

π/4

sec

2

xtan

2

1

dx

Now, let z=tanx ⟹dz=sec

2

xdx

And at x=0,z=0 and at x=

4

π

,z=1

Now, integration becomes ∫

0

1

z

dz

=

3

2

[z

2

3

]

0

1

=

3

2