Answered: find an antiderivative for each…

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter3: Functions

Section3.CM: Cumulative Review Exercises

Problem 38CM

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Question

find an antiderivative for each function. Do as many
as you can mentally. Check your answers by differentiation. -3x^-4

Expert Solution

Step 1

We have to find antiderivative and have to check the answer by derivative for the function:

$- 3 x^{- 4}$

We know the formula of integration,

$\int x^{n} d x = \frac{x^{n + 1}}{n + 1} + C$

Where, $C$ is an arbitrary constant.

So applying above formula,

$\begin{array}{rcl} \int - 3 x^{- 4} d x & = & - 3 \int x^{- 4} d x \\ = & - 3 (\frac{x^{- 4 + 1}}{- 4 + 1}) + C \\ = & - 3 \times \frac{x^{- 3}}{- 3} + C \\ = & x^{- 3} + C \end{array}$

Hence, antiderivative of the function is $x^{- 3} + C$ .

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