1 / | | 2 | x *cos(3*x) dx | / 0
Integral(x^2*cos(3*x), (x, 0, 1))
Use integration by parts:
Let and let .
Then .
To find :
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 cosine is sine:
So, the result is:
Now substitute back in:
Now evaluate the sub-integral.
Use integration by parts:
Let and let .
Then .
To find :
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:
Now evaluate the sub-integral.
The integral of a constant times a function is the constant times the integral of the function:
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 cosine is sine:
So, the result is:
Now substitute back in:
So, the result is:
Add the constant of integration:
The answer is:
/ | 2 | 2 2*sin(3*x) x *sin(3*x) 2*x*cos(3*x) | x *cos(3*x) dx = C - ---------- + ----------- + ------------ | 27 3 9 /
2*cos(3) 7*sin(3) -------- + -------- 9 27
=
2*cos(3) 7*sin(3) -------- + -------- 9 27
2*cos(3)/9 + 7*sin(3)/27
Use the examples entering the upper and lower limits of integration.