Question

sin⁴x.dx
Integrate the function

Answer 1

HELLO DEAR,

GIVEN function is integral of sin⁴x.dx

$\sf{\Rightarrow \int{sin^2x*sin^2x}\,dx}$

[tex]\sf{\Rightarrow 1/4[\int{(1-cos2x)(1 - cos2x)}\,dx]}[/tex]

[tex]\sf{\Rightarrow 1/4[\int{1+cos^2(2x) - 2cos2x}\,dx]}[/tex]

[tex]\sf{\Rightarrow 1/4[\int{1}\,dx+\int{\frac{1+
cos4x}{2}}\,dx-2\int{cos2x}\,dx]}[/tex]

[tex]\sf{\Rightarrow1/4[x+\frac{x}{2}+\frac{sin4x}{8}- sinx]+c}[/tex]


[tex]\sf{\Rightarrow\frac{3}{4}x+\frac{1}{32}sin4x-
\frac{1}{4}sinx+c}[/tex]

I HOPE ITS HELP YOU DEAR,
THANKS

Answer 2

Step-by-step explanation:

I think it should be helpful to all of you...