Integral of sin(x/2) dx
The solution
Detail solution
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Let u=2x.
Then let du=2dx and substitute 2du:
∫4sin(u)du
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The integral of a constant times a function is the constant times the integral of the function:
∫2sin(u)du=2∫sin(u)du
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The integral of sine is negative cosine:
∫sin(u)du=−cos(u)
So, the result is: −2cos(u)
Now substitute u back in:
−2cos(2x)
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Now simplify:
−2cos(2x)
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Add the constant of integration:
−2cos(2x)+constant
The answer is:
−2cos(2x)+constant
The answer (Indefinite)
[src]
/
|
| /x\ /x\
| sin|-| dx = C - 2*cos|-|
| \2/ \2/
|
/
∫sin(2x)dx=C−2cos(2x)
The graph
2−2cos(21)
=
2−2cos(21)
Use the examples entering the upper and lower limits of integration.