1 / | | (4*cos(x) + sin(3*x) - 8*x) dx | / 0
Integral(4*cos(x) + sin(3*x) - 8*x, (x, 0, 1))
Integrate term-by-term:
The integral of a constant times a function is the constant times the integral of the function:
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:
So, the result is:
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 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:
Add the constant of integration:
The answer is:
/ | 2 cos(3*x) | (4*cos(x) + sin(3*x) - 8*x) dx = C - 4*x + 4*sin(x) - -------- | 3 /
11 cos(3) - -- + 4*sin(1) - ------ 3 3
=
11 cos(3) - -- + 4*sin(1) - ------ 3 3
Use the examples entering the upper and lower limits of integration.