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4.12: Antiderivatives

https://math.libretexts.org/Courses/Coastline_College/Math_C180%3A_Calculus_I_(Everett)/04%3A_Applications_of_Derivatives/4.12%3A_Antiderivatives

At this point, we have seen how to calculate derivatives of many functions and have been introduced to a variety of their applications. We now ask a question that turns this process around: Given a fu...At this point, we have seen how to calculate derivatives of many functions and have been introduced to a variety of their applications. We now ask a question that turns this process around: Given a function f , how do we find a function with the derivative f and why would we be interested in such a function?

4.12: Antiderivatives

https://math.libretexts.org/Courses/Coastline_College/Math_C180%3A_Calculus_I_(Tran)/04%3A_Applications_of_Derivatives/4.12%3A_Antiderivatives

At this point, we have seen how to calculate derivatives of many functions and have been introduced to a variety of their applications. We now ask a question that turns this process around: Given a fu...At this point, we have seen how to calculate derivatives of many functions and have been introduced to a variety of their applications. We now ask a question that turns this process around: Given a function f , how do we find a function with the derivative f and why would we be interested in such a function?

5.1: Antiderivatives and Indefinite Integrals

https://math.libretexts.org/Courses/City_College_of_San_Francisco/CCSF_Calculus/05%3A_Investigating_Integrals/5.01%3A_Antiderivatives_and_Indefinite_Integrals

This section introduces antiderivatives and indefinite integrals, explaining the process of reversing differentiation to find the original function. It covers basic integration rules, notation, and th...This section introduces antiderivatives and indefinite integrals, explaining the process of reversing differentiation to find the original function. It covers basic integration rules, notation, and the concept of the constant of integration. Examples demonstrate finding antiderivatives for various functions, establishing foundational skills for solving integral problems.

4.11: Antiderivatives

https://math.libretexts.org/Courses/Monroe_Community_College/MTH_210_Calculus_I_(Seeburger)/04%3A_Applications_of_Derivatives/4.11%3A_Antiderivatives

At this point, we have seen how to calculate derivatives of many functions and have been introduced to a variety of their applications. We now ask a question that turns this process around: Given a fu...At this point, we have seen how to calculate derivatives of many functions and have been introduced to a variety of their applications. We now ask a question that turns this process around: Given a function f , how do we find a function with the derivative f and why would we be interested in such a function?

4.10: Antiderivatives

https://math.libretexts.org/Courses/Mission_College/Math_3A%3A_Calculus_1_(Sklar)/04%3A_Applications_of_Derivatives/4.10%3A_Antiderivatives

At this point, we have seen how to calculate derivatives of many functions and have been introduced to a variety of their applications. We now ask a question that turns this process around: Given a fu...At this point, we have seen how to calculate derivatives of many functions and have been introduced to a variety of their applications. We now ask a question that turns this process around: Given a function f , how do we find a function with the derivative f and why would we be interested in such a function?

5.3: Antiderivatives & the Indefinite Integral

https://math.libretexts.org/Courses/Penn_State_University_Greater_Allegheny/Math_140%3A_Calculus_1_(Gaydos)/05%3A_Integration/5.03%3A_Antiderivatives

At this point, we have seen how to calculate derivatives of many functions and have been introduced to a variety of their applications. We now ask a question that turns this process around: Given a fu...At this point, we have seen how to calculate derivatives of many functions and have been introduced to a variety of their applications. We now ask a question that turns this process around: Given a function f , how do we find a function with the derivative f and why would we be interested in such a function?

4.11: Antiderivatives

https://math.libretexts.org/Courses/City_University_of_New_York/Calculus_I_(CUNY)/04%3A_Applications_of_Derivatives/4.11%3A_Antiderivatives

At this point, we have seen how to calculate derivatives of many functions and have been introduced to a variety of their applications. We now ask a question that turns this process around: Given a fu...At this point, we have seen how to calculate derivatives of many functions and have been introduced to a variety of their applications. We now ask a question that turns this process around: Given a function f , how do we find a function with the derivative f and why would we be interested in such a function?

4.9: Antiderivatives

https://math.libretexts.org/Courses/Chabot_College/MTH_1%3A_Calculus_I/04%3A_Applications_of_Derivatives/4.09%3A_Antiderivatives

At this point, we have seen how to calculate derivatives of many functions and have been introduced to a variety of their applications. We now ask a question that turns this process around: Given a fu...At this point, we have seen how to calculate derivatives of many functions and have been introduced to a variety of their applications. We now ask a question that turns this process around: Given a function f , how do we find a function with the derivative f and why would we be interested in such a function?

4.12: Antiderivatives

https://math.libretexts.org/Courses/Coastline_College/Math_C180%3A_Calculus_I_(Nguyen)/04%3A_Applications_of_Derivatives/4.12%3A_Antiderivatives

At this point, we have seen how to calculate derivatives of many functions and have been introduced to a variety of their applications. We now ask a question that turns this process around: Given a fu...At this point, we have seen how to calculate derivatives of many functions and have been introduced to a variety of their applications. We now ask a question that turns this process around: Given a function f , how do we find a function with the derivative f and why would we be interested in such a function?

5.3: The Fundamental Theorem and Antidifferentiation

https://math.libretexts.org/Courses/Chabot_College/MTH_15%3A_Applied_Calculus_I/05%3A_The_Integral/5.03%3A_The_Fundamental_Theorem_and_Antidifferentiation

We can tell, though, from the graph that the area from

$x = 0$ to

$x = 1$ is about the same as the area from

$x = 1$ to

$x = 3$ , so we would expect the net area from

$x = 0$ to

$x = 3$ to ...We can tell, though, from the graph that the area from

$x = 0$ to

$x = 1$ is about the same as the area from

$x = 1$ to

$x = 3$ , so we would expect the net area from

$x = 0$ to

$x = 3$ to be close to 0.

3.3: The Fundamental Theorem and Antidifferentiation

https://math.libretexts.org/Bookshelves/Calculus/Applied_Calculus_(Calaway_Hoffman_and_Lippman)/03%3A_The_Integral/3.03%3A_The_Fundamental_Theorem_and_Antidifferentiation

We can tell, though, from the graph that the area from

$x = 0$ to

$x = 1$ is about the same as the area from

$x = 1$ to

$x = 3$ , so we would expect the net area from

$x = 0$ to

$x = 3$ to ...We can tell, though, from the graph that the area from

$x = 0$ to

$x = 1$ is about the same as the area from

$x = 1$ to

$x = 3$ , so we would expect the net area from

$x = 0$ to

$x = 3$ to be close to 0.

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