x / | | (cos(x) - x*sin(x))*y dx | / x0
Integral((cos(x) - x*sin(x))*y, (x, x0, x))
The integral of a constant times a function is the constant times the integral of the function:
Integrate term-by-term:
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 sine is negative cosine:
Now evaluate the sub-integral.
The integral of a constant times a function is the constant times the integral of the function:
The integral of cosine is sine:
So, the result is:
So, the result is:
The integral of cosine is sine:
The result is:
So, the result is:
Add the constant of integration:
The answer is:
/ | | (cos(x) - x*sin(x))*y dx = C + x*y*cos(x) | /
x*y*cos(x) - x0*y*cos(x0)
=
x*y*cos(x) - x0*y*cos(x0)
x*y*cos(x) - x0*y*cos(x0)
Use the examples entering the upper and lower limits of integration.