1 / | | 2 | x *sin(4*x)*1 dx | / 0
Integral(x^2*sin(4*x)*1, (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 sine is negative cosine:
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 cosine is sine:
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 sine is negative cosine:
So, the result is:
Now substitute back in:
So, the result is:
Add the constant of integration:
The answer is:
/ | 2 | 2 cos(4*x) x *cos(4*x) x*sin(4*x) | x *sin(4*x)*1 dx = C + -------- - ----------- + ---------- | 32 4 8 /
1 7*cos(4) sin(4) - -- - -------- + ------ 32 32 8
=
1 7*cos(4) sin(4) - -- - -------- + ------ 32 32 8
Use the examples entering the upper and lower limits of integration.