Asked by mat
Find the integral.
∫ -10 x sin x^2 dx
∫ -10 x sin x^2 dx
Answers
Answered by
Reiny
wouldn't that just be
5 cos(x^2) + c ?
5 cos(x^2) + c ?
Answered by
mat
Yes, but how would i show the work.
Answered by
Reiny
some patterns you should just recognize.
I know how to differentiate and integrate sin (?),
but in both cases the derivative of the "angle" which would be the x from the x^2 has to be considered.
Sure enough, the derivative of x^2, which would be 2x , is hanging around at the front as a multiple
( 5(2x) = 10x)
Formal way:
let x^2 = u
2x = du/dx
dx = du/(2x)
∫ -10 x sin x^2 dx
= ∫ -10 x sin (u) (du/(2x))
= ∫ -5 sin (u) du
= 5 cos(u) + c
= 5 cos(x^2) + c
I know how to differentiate and integrate sin (?),
but in both cases the derivative of the "angle" which would be the x from the x^2 has to be considered.
Sure enough, the derivative of x^2, which would be 2x , is hanging around at the front as a multiple
( 5(2x) = 10x)
Formal way:
let x^2 = u
2x = du/dx
dx = du/(2x)
∫ -10 x sin x^2 dx
= ∫ -10 x sin (u) (du/(2x))
= ∫ -5 sin (u) du
= 5 cos(u) + c
= 5 cos(x^2) + c
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