How do you prove integration gives the area under a curve?
How do definite integrals give you the area under a curve? I understand how to find the area of a curve for something simple like $y = x^3 - 6x^2 +9x$ between 0 - 3 but my question is why does it work and how can you prove it?
87
Answer
Answers can only be viewed under the following conditions:
- The questioner was satisfied with and accepted the answer, or
- The answer was evaluated as being 100% correct by the judge.
2.1K
The answer is accepted.
Join Matchmaticians Affiliate Marketing
Program to earn up to a 50% commission on every question that your affiliated users ask or answer.
- answered
- 847 views
- $10.00
Related Questions
- Prove the trig identity $\sec x- \sin x \tan x =\frac{1}{\sec x}$
- You have a piece of 8-inch-wide metal which you are going to make into a gutter by bending up 3 inches on each side
- Is $\int_1^{\infty}\frac{x+\sqrt{x}+\sin x}{x^2-x+1}dx$ convergent?
- Find equation of the tangent line using implicit differentiation
- Use Green’s theorem to compute $\int_C x^2 ydx − xy^2 dy$ where $C$ is the circle $x^2 + y ^2 = 4$ oriented counter-clockwise.
- Solution to Stewart Calculus
- Volume of the solid of revolution
- Calculus 3 Challeng problems