Coursify | AI-Generated Courses

Coursify

Create New Course Gallery Contact

Calculus

Unit 1

Unit 1: Differentiation

Introduction to Differentiation Derivatives Visualizing Differentiation

Unit 2

Unit 2: Integration

Introduction to Integration Integrals Visualizing Integration

Unit 3

Unit 3: Multivariable

Introduction to Multivariable Calculus Multivariable Functions Visualizing Multivariable Calculus

Unit 2 • Chapter 1

Introduction to Integration

Video Summary

This video introduces the concept of integral calculus. It starts with a simple question: how to find the area under a curve. Then it discusses how to approximate the area using rectangles. Finally, it introduces the concept of integral as the limit of the sum of an infinite number of infinitesimally thin things.

Knowledge Check

What is the fundamental theorem of calculus?

a transform that converts a function into a form that describes the frequencies present in the original function

infinite sum of terms that approximate a function as a polynomial

mathematical function that can be formally defined as an improper Riemann integral

certain kind of approximation of an integral by a finite sum

What is the relationship between integration and derivatives?

integration is the inverse of derivatives

integration is the same as derivatives

integration is not related to derivatives

integration is the opposite of derivatives

What is the Riemann sum?

a way to approximate the area under a curve using rectangles

a way to approximate the area under a curve using circles

a way to approximate the area under a curve using trapezoids

a way to approximate the area under a curve using triangles

Calculus

Introduction to Integration

Video Summary

Knowledge Check

.css-1hnz6hu{position:static;}.css-1hnz6hu::before{content:'';cursor:inherit;display:block;position:absolute;top:0px;left:0px;z-index:0;width:100%;height:100%;}Visualizing Differentiation

Integrals

Visualizing Differentiation