Question

Find an antiderivative. $$f(t)=2 t^{2}+3 t^{3}+4 t^{4}$$

Name: Problem 18, Chapter 6: Calculus Single Variable
Uploaded: 2021-04-29T17:15:00-08:00
Duration: 1 min 39 s
Channel: Prashansha Kaushik
Description: Find an antiderivative. f(t)=2 t^2+3 t^3+4 t^4

   Find an antiderivative.
$$f(t)=2 t^{2}+3 t^{3}+4 t^{4}$$

Calculus Single Variable

Deborah… 7th Edition

Chapter 6, Problem 18

Instant Answer

Solved by Expert Prashansha Kaushik

04/29/2021

Step 1

We need to find an antiderivative of this function. The antiderivative of a function is represented as the integral of the function. So, we need to find the integral of $f(t)$. Show more…

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Find an antiderivative. $$f(t)=2 t^{2}+3 t^{3}+4 t^{4}$$

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Key Concepts

Antiderivative

An antiderivative of a function is another function whose derivative is equal to the original function. Finding an antiderivative is essentially the process of reversing differentiation, and it is central to solving problems in calculus that involve integration.

Indefinite Integral

The process of finding an antiderivative is referred to as indefinite integration. It represents the collection of all antiderivatives of a function, typically written with a constant of integration, since differentiating a constant results in zero.

Power Rule for Integration

The power rule for integration is a fundamental technique used to integrate functions of the form t^n. According to this rule, the integral of t^n with respect to t is t^(n+1)/(n+1) plus a constant, provided n is not equal to -1. This rule is particularly useful when integrating polynomial functions.

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