Relation between integration and differentiation?

leojun · Feb 13, 2015

relation between integration and differentiation ?
how is instantaneous slope(differentiation) related to area under the curve(integration) ?

thank you!

DEvens · Feb 13, 2015

http://en.wikipedia.org/wiki/Fundamental_theorem_of_calculus

Cruz Martinez · Feb 13, 2015

How about this video?

symbolipoint · Feb 13, 2015

Cruz Martinez said:

How about this video?

Within the first 1 and a half minutes, the caption shown told the whole idea: We found slope by subtracting heights. That makes the area function easier to understand and for how it is used to instruct the meaning of integration.

Relation between integration and differentiation?

Discussion

Undergrad Why ##a^0=1##?

Undergrad Finding the minimum distance between two curves

Undergrad Best way to numerically solve this system of equations?

High School Arc Length for Hyperbolic Sin

Undergrad Why is ##x=e^y## the inverse of ##y=\int_1^x \frac{1}{t} dt##?

Undergrad Correct Upper/Lower limits for continuation of solutions for ODE

Graduate About ellipticity and a proof that a system of PDEs is elliptic

Graduate Leibniz Rule Videos on Digital-University

Insights Revisiting the Velocity-Time Function

Insights Remote Operated Gate Control System

Insights AI Enriched Problem Solving

Insights Thinking Outside The Box Versus Knowing What’s In The Box

Insights Why Entangled Photon-Polarization Qubits Violate Bell’s Inequality

Insights Quantum Entanglement is a Kinematic Fact, not a Dynamical Effect

Relation between integration and differentiation?

Discussion

Similar threads

Graduate Understanding the Relationship Between Integration and Anti-differentiation

Insights The Amazing Relationship Between Integration And Euler’s Number

Undergrad Are Integration and Differentiation True Opposites in Calculus?

Graduate Abstractions of integration and differentiation

Graduate Website title: Formal Relation Between Integrals of y=f(x) and y=x

Undergrad Difference between integral and antiderivative?

Undergrad Why does the area under 1/x from 1 to x equal ln x?

Undergrad Integration of differential forms

Undergrad What Are Integration and Differentiation in Calculus?

Graduate Relationships between integration limits of Maxwell Equation