1 / | | 7 | sin (x) dx | / 0
Rewrite the integrand:
There are multiple ways to do this integral.
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:
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:
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:
The integral of sine is negative cosine:
The result is:
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:
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:
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:
The integral of sine is negative cosine:
The result is:
Add the constant of integration:
The answer is:
/ | 5 7 | 7 3 3*cos (x) cos (x) | sin (x) dx = C + cos (x) - cos(x) - --------- + ------- | 5 7 /
5 7 16 3 3*cos (1) cos (1) -- + cos (1) - cos(1) - --------- + ------- 35 5 7
=
5 7 16 3 3*cos (1) cos (1) -- + cos (1) - cos(1) - --------- + ------- 35 5 7
Use the examples entering the upper and lower limits of integration.