Question

Evaluate the integrals. $$ \int(-x) d x $$

   Evaluate the integrals.
$$
\int(-x) d x
$$

Finite Mathematics and Applied Calculus

Finite Mathematics and Applied Calculus

Stefan Waner, Steven… 5th Edition

Chapter 13, Problem 6

Instant Answer

Solved by Expert Rukhmani Jain

10/01/2021

Step 1

We can rewrite this as $-1 \int x dx$ because the constant multiple -1 can be factored out of the integral. Show more…

Show all steps

lock

Thanks for your feedback!

Evaluate the integrals. $$ \int(-x) d x $$

Play audio

Feedback

Powered by NumerAI

Rukhmani Jain and 64 other subject Calculus 1 / AB educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Constant of Integration

When performing indefinite integration, an arbitrary constant, often represented as C, is added to the result. This constant accounts for the fact that differentiation of a constant results in zero, so any constant could have been present in the original antiderivative.

Power Rule for Integration

The power rule is a fundamental technique used in integration to compute the antiderivative of functions in the form x^n. It states that ?x^n dx = x^(n+1)/(n+1) + C for any real number n ? -1, making it a quick method for integrating polynomial functions.

Linearity of Integration

The linearity property of integration indicates that the integral of a constant multiplied by a function is equal to the constant multiplied by the integral of the function, and that integration is distributive over addition. This property simplifies the integration process by allowing individual terms to be integrated separately.

Indefinite Integration

Indefinite integration is the process of finding a function, called the antiderivative, whose derivative is equal to the integrand. It represents a family of functions differing by an arbitrary constant, capturing all possible antiderivatives of the given function.

Antiderivative

An antiderivative of a function is another function whose derivative equals the original function. In the context of integration, finding an antiderivative is equivalent to performing the integration operation, and the result includes an arbitrary constant to account for all possible functions that differentiate to the same integrand.

Recommended Videos

Transcript

Ace is your personal tutor. It breaks down any question with clear steps so you can learn.

Start Using Ace

Continue solving this problem

Create a free account to:

View full step-by-step solution
Ask follow-up questions with Ace AI
Save progress and study later