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Fundamental Theorem of Calculus basically shows the relation between differentiation and integration.

The theorem has two parts:

Part I : First Fundamental Theorem of Calculus (FTC1 )

Part 2: Second Fundamental Theorem of Calculus (FTC2)

FTC1 states that differentiation and integration are inverse of each other. It also relates antiderivative concept with area problem.

To calculate the derivative of an integral between bounds using FTC1 , we just plug in an x value for the t variable and the answer ends up being the same.

The following infographic explains how to solve problems based on First Fundamental Theorem of Calculus.

[actucation-blog]

How to do Partial Fraction Decomposition?

Partial Fraction Decomposition is an algebraic technique used to convert a complex rational function into a sum of two or more simplex fractions.

A rational function is a function where two polynomials are in division. In some cases where the degree of denominator is greater than or equal to numerator, direct integration is quite difficult. To deal with such problems, we adopt a technique called Partial Fraction Decomposition.

The following infographic will help you in understanding how to integrate complex rational function having linear repeated factors