7 / | | 2 | (7 - x) dx | / 4807 ---- 1000
Integral((7 - x)^2, (x, 4807/1000, 7))
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:
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 is the constant times the variable of integration:
The result is:
Now simplify:
Add the constant of integration:
The answer is:
/ | 3 | 2 (7 - x) | (7 - x) dx = C - -------- | 3 /
3515561019 ---------- 1000000000
=
3515561019 ---------- 1000000000
3515561019/1000000000
Use the examples entering the upper and lower limits of integration.