1/4 / | | asin(2*x) dx | / 0
Integral(asin(2*x), (x, 0, 1/4))
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:
Use integration by parts:
Let and let .
Then .
To find :
The integral of a constant is the constant times the variable of integration:
Now evaluate the sub-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:
So, the result is:
Now substitute back in:
Use integration by parts:
Let and let .
Then .
To find :
The integral of a constant is the constant times the variable of integration:
Now evaluate the sub-integral.
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:
Add the constant of integration:
The answer is:
__________ / / 2 | \/ 1 - 4*x | asin(2*x) dx = C + ------------- + x*asin(2*x) | 2 /
___ 1 \/ 3 pi - - + ----- + -- 2 4 24
=
___ 1 \/ 3 pi - - + ----- + -- 2 4 24
-1/2 + sqrt(3)/4 + pi/24
Use the examples entering the upper and lower limits of integration.