1 / | | _________ | / 3*x | / 1 + --- dx | \/ 2 | / 0
Integral(sqrt(1 + 3*x/2), (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:
The integral of is when :
So, the result is:
Now substitute back in:
Rewrite the integrand:
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 simplify:
Add the constant of integration:
The answer is:
/ 3/2 | / 3*x\ | _________ 4*|1 + ---| | / 3*x \ 2 / | / 1 + --- dx = C + -------------- | \/ 2 9 | /
____ 4 5*\/ 10 - - + -------- 9 9
=
____ 4 5*\/ 10 - - + -------- 9 9
-4/9 + 5*sqrt(10)/9
Use the examples entering the upper and lower limits of integration.