Definite Integral by Definition

1. Dec 9, 2015

OmniNewton

1. The problem statement, all variables and given/known data
Let A be the area of the region that lies under the graph of f(x) = 2x 2 + 5 between x = 0 and x = 4. Find an expression for A using n rectangles. Then evaluate this expression.

2. Relevant equations
h= (4/n)

3. The attempt at a solution

The problem I am having is I do not know how to simplify this limit further after factoring out the h.

Last edited by a moderator: Dec 9, 2015
2. Dec 9, 2015

BvU

$f(a+h)$ is not $5+h$ but $2(a+h)^2+5$ !?

Aren't you supposed to find $A(n)$ ?

3. Dec 9, 2015

OmniNewton

You are right about 2(a+h)^2+5. So you would suggest to convert this limit all to "n" and evaluate the limit as n ---> infinity?

4. Dec 9, 2015

BvU

If you have faithfully rendered the problem statement, the answer is an expression. Something like $\displaystyle A = \sum_{i=1}^n \ ... \$

The way I read it you want to work out e.g. the middle riemann sum

5. Dec 11, 2015

Ray Vickson

I cannot read your formula for f(x). Is it $f(x) = 2x^2 + 5$? $f(x) = (2x)^2 + 5$? Something else? If it really does involve the second power (and if you don't want to use either LaTeX or the formula template in the top green panel, then you need to use "^" instead, as in 2 x^2 + 5 or (2x)^2 + 5.

6. Dec 11, 2015

BvU

Well, the book answer helps you out, Ray

7. Dec 11, 2015

Ray Vickson

Well, of course I can guess what the OP means, but the whole point is that I should not need to. He/she needs to adhere to the standard notation; that's why it was invented.

8. Dec 12, 2015

BvU

Agree.
But it looks as if Newt is out of the picture ?