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