1 / | | sin(3*x) | ------------ dx | __________ | \/ cos(3*x) | / 0
Integral(sin(3*x)/sqrt(cos(3*x)), (x, 0, 1))
There are multiple ways to do this integral.
Let .
Then let and substitute :
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:
Now substitute back in:
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 a constant is the constant times the variable of integration:
So, the result is:
Now substitute back in:
Add the constant of integration:
The answer is:
/ | __________ | sin(3*x) 2*\/ cos(3*x) | ------------ dx = C - -------------- | __________ 3 | \/ cos(3*x) | /
________ 2 2*\/ cos(3) - - ------------ 3 3
=
________ 2 2*\/ cos(3) - - ------------ 3 3
2/3 - 2*sqrt(cos(3))/3
(0.579862216335156 - 0.795858425143173j)
(0.579862216335156 - 0.795858425143173j)
Use the examples entering the upper and lower limits of integration.