Integral of cos(2*pi*x)f(t) dy
The solution
Detail solution
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The integral of a constant times a function is the constant times the integral of the function:
∫ftcos(2πx)dx=ft∫cos(2πx)dx
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Let u=2πx.
Then let du=2πdx and substitute 2πdu:
∫4π2cos(u)du
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The integral of a constant times a function is the constant times the integral of the function:
∫2πcos(u)du=2π∫cos(u)du
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The integral of cosine is sine:
∫cos(u)du=sin(u)
So, the result is: 2πsin(u)
Now substitute u back in:
2πsin(2πx)
So, the result is: 2πftsin(2πx)
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Add the constant of integration:
2πftsin(2πx)+constant
The answer is:
2πftsin(2πx)+constant
The answer (Indefinite)
[src]
/
| f*t*sin(2*pi*x)
| cos(2*pi*x)*f*t dx = C + ---------------
| 2*pi
/
2πftsin(2πx)
2πfsin(2π)t
=
Use the examples entering the upper and lower limits of integration.