pi -- 2 / | | 10 9 | sin (x)*cos (x) dx | / 0
Integral(sin(x)^10*cos(x)^9, (x, 0, pi/2))
Rewrite the integrand:
There are multiple ways to do this integral.
Let .
Then let and substitute :
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 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 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 integral of is when :
The result is:
Now substitute back in:
Rewrite the integrand:
Integrate term-by-term:
Let .
Then let and substitute :
The integral of is when :
Now substitute back in:
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 is when :
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 is when :
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 is when :
Now substitute back in:
So, the result is:
Let .
Then let and substitute :
The integral of is when :
Now substitute back in:
The result is:
Rewrite the integrand:
Integrate term-by-term:
Let .
Then let and substitute :
The integral of is when :
Now substitute back in:
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 is when :
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 is when :
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 is when :
Now substitute back in:
So, the result is:
Let .
Then let and substitute :
The integral of is when :
Now substitute back in:
The result is:
Now simplify:
Add the constant of integration:
The answer is:
/ | 13 17 11 19 15 | 10 9 4*sin (x) 4*sin (x) sin (x) sin (x) 2*sin (x) | sin (x)*cos (x) dx = C - ---------- - ---------- + -------- + -------- + ---------- | 13 17 11 19 5 /
128 ------ 230945
=
128 ------ 230945
128/230945
Use the examples entering the upper and lower limits of integration.