1 / | | / 2\ | x*acos\x / dx | / 3/4
Integral(x*acos(x^2), (x, 3/4, 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.
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:
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.
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:
/ ________ | / 4 2 / 2\ | / 2\ \/ 1 - x x *acos\x / | x*acos\x / dx = C - ----------- + ----------- | 2 2 /
___ 9*acos(9/16) 5*\/ 7 - ------------ + ------- 32 32
=
___ 9*acos(9/16) 5*\/ 7 - ------------ + ------- 32 32
-9*acos(9/16)/32 + 5*sqrt(7)/32
Use the examples entering the upper and lower limits of integration.