In google type :
integration calculator online emathhelp
when you see list of results click on :
Integral Calculator with Steps - eMathHelp
When page be open In rectangle type :
sinx^2.xdx then clic button CALCULATE
You will se solution step - by -step
Integrate sinx^2.xdx???
3 answers
we know that
cos 2x = 1 - 2sin^2 x
2sin^2 x = 1 - cos 2x
sin^2 x = 1/2 - (1/2)cos(2x)
so integral(sin^2 x)dx
= integral( 1/2 - (1/2)cos(2x) ) dx
= (1/2)x - (1/4)sin(2x) + costant
cos 2x = 1 - 2sin^2 x
2sin^2 x = 1 - cos 2x
sin^2 x = 1/2 - (1/2)cos(2x)
so integral(sin^2 x)dx
= integral( 1/2 - (1/2)cos(2x) ) dx
= (1/2)x - (1/4)sin(2x) + costant
To make things a bit clearer,
∫sin(x^2) x dx
let
u = x^2
du = 2x dx
and you have
∫1/2 sin(u) du
not so hard, eh?
∫sin(x^2) x dx
let
u = x^2
du = 2x dx
and you have
∫1/2 sin(u) du
not so hard, eh?