1 / | | f*(x + 4)*sin(x) dx | / 0
Integral(f*(x + 4)*sin(x), (x, 0, 1))
The integral of a constant times a function is the constant times the integral of the function:
There are multiple ways to do this integral.
Rewrite the integrand:
Integrate term-by-term:
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:
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 result is:
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:
Add the constant of integration:
The answer is:
/ | | f*(x + 4)*sin(x) dx = C + f*(-4*cos(x) - x*cos(x) + sin(x)) | /
Use the examples entering the upper and lower limits of integration.