1 / | | (sin(5*x) - sin(5*a)) dx | / 0
Integral(sin(5*x) - sin(5*a), (x, 0, 1))
Integrate term-by-term:
The integral of a constant is the constant times the variable of integration:
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 sine is negative cosine:
So, the result is:
Now substitute back in:
The result is:
Add the constant of integration:
The answer is:
/ | cos(5*x) | (sin(5*x) - sin(5*a)) dx = C - -------- - x*sin(5*a) | 5 /
1 cos(5) - - sin(5*a) - ------ 5 5
=
1 cos(5) - - sin(5*a) - ------ 5 5
1/5 - sin(5*a) - cos(5)/5
Use the examples entering the upper and lower limits of integration.