(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

a) Write down the definition of the definite integral in terms of a limiting procedure of elementary areas

b) Write down the definition of the indefinate integral

c) Show that the derivative of an indefinite integral of f(x) is f(x)

3. The attempt at a solution

I'm not really sure what they mean in part a. Is it something like if there is a function y(x) the area under the curve between limits x=b and x=a where

b > a. If it is divided in to strips of Area [tex]\ y \delta x = \delta A [/tex] then [tex]\ y = limit \delta x [/tex] goes to 0 [tex]\frac{\delta x}{\delta a} = \frac{dA}{dx} [/tex]

so A = integral from x=b to x=a ydx

An indefinite integral is a family of functions ie. F(x) + C whose derivatives are all f(x)

If the integral of f(x)dx is F(x) + C , then the derivative of F(x) + C is f(x) + 0

= f(x)

I'm really not sure about these, could someone help me out please.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Theory question Differentiation / Integration

**Physics Forums | Science Articles, Homework Help, Discussion**