Find the antiderivative of the following function.f(x)=200f\left(x\right)=200f(x)=200

F(x)=200x+CF\left(x\right)=200x+CF(x)=200x+C

Find the antiderivative of the following function. f ( x ) = 200 f\left(x\right)=200 f ( x ) = 200

this problem, we're asked to find the antiderivative of the following function. Now recall that if we want to find the antiderivative of a function, what we need to do is think about what derivative would give us this function. Now you can see we just have the constant 200 here. And if I think about it, if I were to take the derivative of 200 x, that x would come off of the derivative, wouldn't take you the derivative, and give us just 200. So 200 x would be the antiderivative, and don't forget we have to add the constant of integration, c. So this right here would be the solution to this problem. Hope you found this video helpful.

Find the antiderivative of the following function.f(x)=200f\left(x\right)=200f(x)=200

F(x)=200x+CF\left(x\right)=200x+CF(x)=200x+C

F(x)=200+CF\left(x\right)=200+CF(x)=200+C

F(x)=200xF\left(x\right)=200xF(x)=200x

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0. Functions4h 53m

Introduction to Functions
16m

Piecewise Functions
10m

Properties of Functions
9m

Common Functions
1h 8m

Transformations
5m

Combining Functions
27m

Exponent Rules
32m

Exponential Functions
28m

Logarithmic Functions
24m

Properties of Logarithms
34m

Exponential & Logarithmic Equations
35m

1. Limits and Continuity2h 2m

Introduction to Limits
41m

Finding Limits Algebraically
40m

Continuity
40m

2. Intro to Derivatives1h 33m

Tangent Lines and Derivatives
30m

Derivatives as Functions
14m

Basic Graphing of the Derivative
23m

Differentiability
26m

3. Techniques of Differentiation2h 18m

Basic Rules of Differentiation
43m

Higher Order Derivatives
12m

Product and Quotient Rules
55m

The Chain Rule
27m

4. Derivatives of Exponential & Logarithmic Functions1h 16m

Derivatives of Exponential & Logarithmic Functions
1h 16m

5. Applications of Derivatives2h 19m

Implicit Differentiation
27m

Logarithmic Differentiation
17m

Related Rates
59m

Differentials
21m

Linearization
13m

6. Graphical Applications of Derivatives6h 0m

Intro to Extrema
21m

The First Derivative Test
1h 20m

Concavity
1h 0m

The Second Derivative Test
22m

Curve Sketching
44m

Finding Global Extrema
29m

Applied Optimization
1h 41m

7. Antiderivatives & Indefinite Integrals48m

Antiderivatives
17m

Indefinite Integrals
31m

8. Definite Integrals4h 30m

Estimating Area with Finite Sums
42m

Riemann Sums
1h 16m

Introduction to Definite Integrals
20m

Fundamental Theorem of Calculus
25m

Average Value of a Function
17m

Substitution for Indefinite Integrals
55m

Substitution for Definite Integrals
32m

9. Graphical Applications of Integrals1h 43m

Area Between Curves
1h 19m

Introduction to Volume & Disk Method
23m

10. Integrals of Inverse, Exponential, & Logarithmic Functions21m

Integrals of Exponential Functions
14m

Integrals Involving Logarithmic Functions
7m

11. Techniques of Integration2h 7m

Integration by Parts
1h 37m

Improper Integrals
29m

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Angles
29m

Trigonometric Functions on Right Triangles
1h 8m

Solving Right Triangles
23m

Trigonometric Functions on the Unit Circle
1h 19m

Graphs of Sine & Cosine
46m

Graphs of Other Trigonometric Functions
32m

Trigonometric Identities
52m

Derivatives of Trig Functions
42m

Integrals of Basic Trig Functions
28m

Integrals of Other Trig Functions
10m

13: Intro to Differential Equations2h 23m

Basics of Differential Equations
43m

Slope Fields
19m

Separable Differential Equations
1h 21m

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Sequences
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Review of Factorials
11m

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44m

15. Power Series2h 19m

Power Series & Taylor Series
2h 19m

16. Probability & Calculus45m

Continuous Probability Models
45m

7. Antiderivatives & Indefinite Integrals

Antiderivatives

Business Calculus

7. Antiderivatives & Indefinite Integrals

Antiderivatives

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Find the antiderivative of the following function.
$f$\left$(x$\right$)=200$

$F$\left$(x$\right$)=0$

$F$\left$(x$\right$)=200+C$

$F$\left$(x$\right$)=200x$

$F$\left$(x$\right$)=200x+C$

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Problema precedenteProssimo problema

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Recognize that finding the antiderivative of a function involves reversing the process of differentiation. This means we are looking for a function F(x) such that F'(x) = f(x).

The given function is f(x) = 200. This is a constant function, and the antiderivative of a constant is the constant multiplied by x, plus an arbitrary constant of integration, C.

Using the antiderivative rule for constants, ∫a dx = ax + C, apply this to f(x) = 200. Here, a = 200.

The antiderivative of 200 is 200x. Don't forget to add the constant of integration, C, because the antiderivative is not unique without it.

Thus, the antiderivative of f(x) = 200 is F(x) = 200x + C.