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