1 / | | /x\ /x\ | 2*sin|-|*cos|-| dx | \2/ \2/ | / 0
Integral((2*sin(x/2))*cos(x/2), (x, 0, 1))
There are multiple ways to do this integral.
Let .
Then let and substitute :
The integral of is when :
Now substitute back in:
Let .
Then let and substitute :
The integral of a constant times a function is the constant times the integral of the function:
The integral of is when :
So, the result is:
Now substitute back in:
Let .
Then let and substitute :
The integral of a constant times a function is the constant times the integral of the function:
Let .
Then let and substitute :
The integral of a constant times a function is the constant times the integral of the function:
The integral of is when :
So, the result is:
Now substitute back in:
So, the result is:
Now substitute back in:
Let .
Then let and substitute :
The integral of a constant times a function is the constant times the integral of the function:
The integral of is when :
So, the result is:
Now substitute back in:
Now simplify:
Add the constant of integration:
The answer is:
/ | | /x\ /x\ 2/x\ | 2*sin|-|*cos|-| dx = C + 2*sin |-| | \2/ \2/ \2/ | /
2 2*sin (1/2)
=
2 2*sin (1/2)
2*sin(1/2)^2
Use the examples entering the upper and lower limits of integration.