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Summary Antiderivatives & Integration Review $5.49
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  3. Senior / 12th Grade
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  5. AP Calculus BC

Summary

Summary Antiderivatives & Integration Review

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  • Course
  • AP Calculus BC
  • Institution
  • Senior / 12th Grade

Provides an introduction and thorough explainer on antiderivatives and integration, including the definition, important rules and how to solve problems using the reverse power rule, constant rule, sum rule and more with example problems.

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  • January 6, 2025
  • 2
  • 2024/2025
  • Summary

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  • Senior / 12th grade
  • AP Calculus BC
  • 4

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Antiderivatives/Integration




Antiderivatives- > "undo" derivatives >
- the opposite operation of
derivatives
antiderivative
-




f(x) = 3x2 derivative
<
f(x) = x3


An antiderivative of a function f(x) is another function F(x) whose derivative

is f(x)
x(F(x)) =
f(x)
The notation for the antiderivative of f(x) is often written the
using
indefinite integral :
(f(x) dx >
- all possible functions F(x) that satisfy
F'(x) = f(x)
The Constant of Integration
Whenever you take the derivative of a function f(x) , adding a constant
(does not change the derivative :
* (f(x) + () (f(x))
=
+ Ex() = f(x) + 0 =
f(x)
The general antiderivative formula is :


=
(f(x)dX
F(x) + C
the constant of integration-
WAYSbewrittenPart,
a
must
-




The Rules
Power Rule : Px" dx =+ C
,
where ne-

1 Identify it the integrand
.
2 Increase the exponent by . . 1




. Divide by the new exponent
3 4 Add constant of integration .




Constant Rule Padx .
=
ax + C where
,
a is a constant
2
1 Recognize
. that the integrand is a constant .




Multiply the constant by x

3
. Add the constant of integration (
Sum Rule : ([f(x) + g(x)]dx f f(x)dx (g(x)dx
=
+




1
. Separate the integral of a sum into the individual integrals
2 .



Integrate each function individually into rules
you
know
.
3 Add the constants of integration which can be combined into one constant
,

2

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