Find the following indefinite integral. ∫ 100 x 99 d x \int100x^{99}dx

this problem, we are asked to find the following indefinite integral, and we are given this function right here that we are integrating with respect to x. Now to solve this problem, what we wanna do is find what the antiderivative is of this integrand that shows up inside the integral. If we can find the antiderivative, we can find the solution to this problem. Now looking at this function, there's something that I notice. For the integrand, notice we have a 100 out in front and then we have this power function where we have x to the 99th. This is one reduced number from that number, so 100 minus 1 would be 99. So it looks like we went through some kind of power rule for the initial derivative. So what I'm going to do is try taking this front number out here, and I'm going to make it the exponent. So we're gonna have x to the 100th power. Now if I were to take this derivative, notice we would get 100 x to the 99th power. So this would give us the integrand. So this right here would be the function that we're looking for. This is the antiderivative, and don't forget to add the constant of integration c. So that right there is the solution to this problem. Let's move on.

Find the following indefinite integral. ∫ 100 x 99 d x \int100x^{99}dx

100 99 x 100 \frac{100}{99}x^{100}

100 99 x 100 + C \frac{100}{99}x^{100}+C

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0. Functions7h 52m
1. Limits and Continuity2h 2m
2. Intro to Derivatives1h 33m
3. Techniques of Differentiation3h 18m
4. Applications of Derivatives2h 38m
5. Graphical Applications of Derivatives6h 2m
6. Derivatives of Inverse, Exponential, & Logarithmic Functions2h 37m
7. Antiderivatives & Indefinite Integrals1h 26m
8. Definite Integrals4h 44m
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10. Physics Applications of Integrals 3h 16m
- Kinematics
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- Work
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11. Integrals of Inverse, Exponential, & Logarithmic Functions2h 34m
12. Techniques of Integration7h 39m
13. Intro to Differential Equations2h 55m
14. Sequences & Series5h 36m
15. Power Series2h 19m
- Introduction to Power Series
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16. Parametric Equations & Polar Coordinates7h 58m

7. Antiderivatives & Indefinite Integrals

Indefinite Integrals

Calculus

7. Antiderivatives & Indefinite Integrals

Indefinite Integrals

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Multiple Choice

Find the following indefinite integral.
$\int 100 x^{99} d x$

$\frac{100}{99} x^{100}$

$x to the 100th power$

$\frac{100}{99} x^{100} + C$

$x^{100} + C$

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Verified step by step guidance

Identify the integral to be solved: ∫100x^{99}dx.

Apply the power rule for integration, which states that ∫x^n dx = (1/(n+1))x^{n+1} + C, where C is the constant of integration.

In this case, the integrand is 100x^{99}. The coefficient 100 can be factored out of the integral, simplifying the expression to 100∫x^{99}dx.

Use the power rule: ∫x^{99}dx = (1/(99+1))x^{99+1} = (1/100)x^{100}.

Multiply the result by the factored coefficient: 100 * (1/100)x^{100} = x^{100}. Add the constant of integration C to get the final expression: x^{100} + C.