1 / | | 3 | sin (x) | ------- dx | 7 | cos (x) | / 0
Rewrite the integrand:
There are multiple ways to do this integral.
Let .
Then let and substitute :
Let .
Then let and substitute :
The integral of a constant times a function is the constant times the integral of the function:
Rewrite the integrand:
Integrate term-by-term:
The integral of is when :
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:
The result is:
So, the result is:
Now substitute back in:
Now substitute back in:
Rewrite the integrand:
Let .
Then let and substitute :
Let .
Then let and substitute :
The integral of a constant times a function is the constant times the integral of the function:
Rewrite the integrand:
Integrate term-by-term:
The integral of is when :
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:
The result is:
So, the result is:
Now substitute back in:
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:
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 is when :
So, the result is:
Now substitute back in:
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 is when :
So, the result is:
Now substitute back in:
The result is:
Now simplify:
Add the constant of integration:
The answer is:
/ | | 3 | sin (x) 1 1 | ------- dx = C - --------- + --------- | 7 4 6 | cos (x) 4*cos (x) 6*cos (x) | /
2 1 2 - 3*cos (1) -- + ------------- 12 6 12*cos (1)
=
2 1 2 - 3*cos (1) -- + ------------- 12 6 12*cos (1)
Use the examples entering the upper and lower limits of integration.