Question

Long hand way to evaluate an definite integral?

Answer 1

The problem is \[\int\limits_{2}^{6} x ^{2} dx\]
the answer doing it the normal way is finding the anti derivative which is x^3/3 then plugging in 6 and 2 and subtracting it. I get an answer of 208/3. my teacher wants this done another way that is harder to do and less efficient. I dont remember the details and would be grateful if someone could explain the other way of solving this.

Answer 2

The only "long way" I can think of for this kind of integral is evaluating it as a Riemann sum.

Answer 3

http://tutorial.math.lamar.edu/Classes/CalcI/DefnOfDefiniteIntegral.aspx
is the formula he has on here. there are some changes though, ours says to use Δ(x)=b-a/n and xi=a+iΔ(x)

Answer 4

Its hurting my brain.

Answer 5

Alright, I'll try to explain this one... Picture the x-axis (I'll provide images). \(a\) and \(b\) are two different x-values. Do you understand why the distance between \(a\) and \(b\) is \(b-a\)?