1 / | | / 2\ | x*asin\x / dx | / 0
Integral(x*asin(x^2), (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:
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 is when :
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:
Add the constant of integration:
The answer is:
/ ________ | / 4 2 / 2\ | / 2\ \/ 1 - x x *asin\x / | x*asin\x / dx = C + ----------- + ----------- | 2 2 /
1 pi - - + -- 2 4
=
1 pi - - + -- 2 4
-1/2 + pi/4
Use the examples entering the upper and lower limits of integration.