Find the following indefinite integral.∫−300dx\int-300dx∫−300dx

− 300 x + C -300x+C − 300 x + C

Find the following indefinite integral. ∫ − 300 d x \int-300dx ∫ − 300 d x

this problem, we're asked to find the following indefinite integral. Now recall that when dealing with these indefinite integrals, what you're in essence doing is finding the antiderivative of this function, the integrand that is inside of the integral, and then you just need to add your cost of integration, same process with the antiderivative, and that's going to give you your result. Now because I can see we have a constant inside the integral, we know that from the rules of antiderivatives as well as just the general rules for integrals, that all you need to do is take this term here and and you need to slap an x on it. Since we're integrating with respect to x, I'm just gonna multiply by x. I know that this is gonna work because if I took the derivative of this whole thing, that x would just come off giving me this negative 300. So that in essence is the antiderivative of this integrand right here, which means negative 300x plus the constant of integration c is going to be the solution to this integral. So that's how you can solve this problem. Hope you found this helpful, and let's move on.

Find the following indefinite integral. ∫ − 300 d x \int-300dx ∫ − 300 d x

− 300 x + C -300x+C − 300 x + C

7. Antiderivatives & Indefinite Integrals

Indefinite Integrals

Calculus

7. Antiderivatives & Indefinite Integrals

Indefinite Integrals

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Multiple Choice

Find the following indefinite integral.
$\int-300dx$

$-300x+C$

$-300x$

$300x+C$

$-300+C$

Verified step by step guidance

Identify the integral to be solved: $ \int -300 \, dx $. This is an indefinite integral, meaning we are looking for a function whose derivative is $-300$.

Recognize that $-300$ is a constant. The integral of a constant $a$ with respect to $x$ is $ax + C$, where $C$ is the constant of integration.

Apply the rule for integrating a constant: $ \int a \, dx = ax + C $. In this case, $a = -300$, so the integral becomes $-300x + C$.

Understand that the constant of integration $C$ is added because the derivative of any constant is zero, and thus it accounts for all possible antiderivatives.

Conclude that the indefinite integral of $-300$ with respect to $x$ is $-300x + C$, where $C$ is an arbitrary constant.

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