1 / | | (4 - x)*cos(x) dx | / 0
Integral((4 - x)*cos(x), (x, 0, 1))
There are multiple ways to do this integral.
Let .
Then let and substitute :
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 cosine is sine:
Now evaluate the sub-integral.
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 substitute back in:
Rewrite the integrand:
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 cosine is sine:
Now evaluate the sub-integral.
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:
Use integration by parts:
Let and let .
Then .
To find :
The integral of cosine is sine:
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 sine is negative cosine:
So, the result is:
Add the constant of integration:
The answer is:
/ | | (4 - x)*cos(x) dx = C - cos(x) + 4*sin(x) - x*sin(x) | /
1 - cos(1) + 3*sin(1)
=
1 - cos(1) + 3*sin(1)
1 - cos(1) + 3*sin(1)
Use the examples entering the upper and lower limits of integration.