Find the general antiderivative F(x)+C for each of the following. f(x)=3 x^2-πx

Name: Problem 10, Chapter 3: Calculus
Uploaded: 2021-06-11T17:45:07-08:00
Duration: 1 min 46 s
Channel: Rukhmani Jain
Description: Find the general antiderivative F(x)+C for each of the following. f(x)=3 x^2-πx

step 1 In this question we have to find the antiderivative of the function f x is equal to 3x squared m

Find the general antiderivative F(x)+C for each of the...

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Key Concepts

Antiderivative

An antiderivative of a function is another function whose derivative equals the original function. In other words, if F(x) is an antiderivative of f(x), then F'(x) = f(x). The process of finding an antiderivative is known as integration, and the set of all antiderivatives is represented by adding an arbitrary constant C, which accounts for the family of functions differing only by a constant.

Power Rule for Integration

The power rule for integration is a fundamental technique used to integrate functions of the form x^n, where n is any real number except -1. It states that the antiderivative of x^n is x^(n+1)/(n+1) plus a constant of integration. This rule greatly simplifies the process of integrating polynomial functions by allowing each term to be integrated individually.

Linearity of Integration

The linearity of integration is an important property that allows the integral of a sum of functions to be computed as the sum of the integrals of each function individually. Additionally, constants can be factored out of integrals. This property not only simplifies the integration of composite functions, such as polynomials, but also reinforces that the process is additive and respects constant multiples.

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