2*pi / | | (-3*y*sin(x) + 12*y*cos(x)) dx | / 0
Integral((-3*y)*sin(x) + (12*y)*cos(x), (x, 0, 2*pi))
Integrate term-by-term:
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:
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:
The result is:
Now simplify:
Add the constant of integration:
The answer is:
/ | | (-3*y*sin(x) + 12*y*cos(x)) dx = C + 3*y*cos(x) + 12*y*sin(x) | /
Use the examples entering the upper and lower limits of integration.