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How to represent functions as a power series

Integral Calculus: Master Advanced Integration Techniques

Integrals

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Antiderivatives

Derivatives and Antiderivatives

Derivative and Antiderivative of a Function

Riemann sum

Riemann Sum

Evaluating integrals with a Riemann sum

Evaluating integrals with a Riemann Sum

Riemann Sum with Trapezoid Approximation

Trapezoidal Approximation of Riemann Sums

Fundamental theorem of calculus

Fundamental Theorem of Calculus Part II

Fundamental Theorem of Calculus Part I

Fundamental Theorem of Calculus

Definite integral

Definite Integral

Integration Techniques

Numerical integration

Numerical Integration

U-Substitution

U-Substitution: Integrating Radical Functions

Not-So-Obvious U-Substitution

Trigonometric substitution

Trigonometric Substitution

Integration of rational functions by partial fractions

Improper integrals

Improper Integrals

Integration by parts

Integration using trigonometric identities

Integration Applications

Areas between curves

Volumes of solids of revolution - Disc method

Volumes of solid with known cross-sections

Volumes of solids of revolution - Shell method

Volumes of solid of revolution - Shell method

Arc length

Average value of a function

Introduction to differential equations

Order and solutions to differential equations

Separable equations

Separable Equations

Applications to differential equations

Modeling with differential equations

Slope fields

Understanding Slope Fields

Euler's method

Euler's Method

Euler"s Method

Euler"s method

Sequence and Series

Introduction to sequences

Monotonic and bounded sequences

Introduction to infinite series

Convergence and divergence of normal infinite series

Convergence & divergence of geometric series

Divergence of Geometric Series

Convergence & divergence of telescoping series

Divergence of harmonic series

Divergence of Harmonic Series

P Series

Convergence and Divergence of P Series

Alternating series test

Alternating Series Test

Convergence of the Alternating Series Test

Divergence test

Divergence Test

Comparison & limit comparison test

Comparison & Limit Comparison Test

Integral test

Integral Test for Series Convergence

Convergence/Divergence of Integral Test

Ratio test

Ratio Test

Convergence & Divergence of Ratio Test

Root test

Root Test

Root Test for Series Convergence

Convergence & Divergence of Root test

Absolute & conditional convergence

Absolute & Conditional Convergence

Radius and interval of convergence with power series

Radius of Convergence of Logarithmic Function

Radius and Interval of Convergence with Power Series

Radius of Convergence of Tangent Function

Functions expressed as power series

Taylor series and Maclaurin series

Approximating functions with Taylor polynomials and error bounds

Parametric Equations and Polar Coordinates

Defining curves with parametric equations

Tangent and concavity of parametric equations

Area of parametric equations

Arc length and surface area of parametric equations

Arc Length of a Parametric Curve

Polar coordinates

Tangents of polar curves

Area of polar curves

Arc length of polar curves

Integral calculus made easy!
Get better marks in calculus class with our complete Integral Calculus help. Our calculus tutors cover all topics you will see in any typical Integration class that deals with single variable functions.

Keeping with your textbook and class, our Integral calculus video lessons walk you through all topics in integral calculus such as, Antiderivative, Integral of trig functions, Definite integral, Indefinite integral, Integration by substitution, Improper integrals and more. Learn the concepts with our tutorials that show you step-by-step solutions to even the hardest integral calculus questions. Then, reinforce your understanding with tons of integral calculus practice.
All our lessons are taught by experienced calculus teachers. Let&apos;s finish your homework in no time, and ACE that exam.

Integral Calculus

sample

math

https://dmn92m25mtw4z.cloudfront.net/img_set/textbook-integral-calculus/v1/textbook-integral-calculus-168w.png

Ex.1

Ex.2

Expressing ln(7−x) as a power series and finding convergence

Ex.3

Expressing the derivative of 1/(1-x) as a power series

Expressing 1/(1-x²) as a power series and finding convergence

Converting 1/(2-x) to a power series and finding convergence

Converting a rational function with x² numerator into a power series

In this section, we will learn how to convert functions into power series. Most of the functions we will be dealing with will be converted into a geometric series. After converting them into a power series, we will find the interval of convergence. Keep in mind that we do not have to check the endpoints of the inequality because we automatically know they will be divergent. Afterwards, we will look at an irregular function and express it as a power series. Integrals will be involved here. We will also take the derivative of a function and express that as a power series.

Convergence & divergence of geometric series 

Functions expressed as power series

What You'll Learn

Convert functions into power series using the geometric series formula

Identify the common ratio r by algebraically manipulating functions

Apply the formula 1/(1-r) = Σ r^n to express functions as infinite series

Determine intervals of convergence from the absolute value of r

Differentiate and integrate power series term by term

Express derivatives and antiderivatives of functions as power series

What You'll Practice

Converting rational functions like 1/(1-x²) into geometric series

Factoring and manipulating denominators to match the 1/(1-r) form

Finding intervals of convergence by solving |r| < 1 inequalities

Integrating power series to express logarithmic functions

Differentiating power series and adjusting series indices

Why This Matters

Before You Start — Make Sure You Can:

This Unit Includes

5 Video lessons

Practice exercises

Skills

Power Series

Geometric Series

Interval of Convergence

Series Representation

Differentiation

Integration

Algebraic Manipulation

Convergence Tests