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Unit: Antiderivatives and the fundamental theorem of calculus

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Antiderivatives and indefinite integrals intro

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Antiderivatives and indefinite integrals
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Antiderivatives and indefinite integrals review
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Fundamental theorem of calculus

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The fundamental theorem of calculus and accumulation functions
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The fundamental theorem of calculus and definite integrals
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Finding derivative with fundamental theorem of calculus
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Fundamental theorem of calculus review
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Proof of fundamental theorem of calculus
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Finding derivative with fundamental theorem of calculus: x is on lower bound
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Finding derivative with fundamental theorem of calculus: x is on both bounds
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Practice
Finding derivative with fundamental theorem of calculusGet 3 of 4 questions to level up!
Finding derivative with fundamental theorem of calculus: chain ruleGet 3 of 4 questions to level up!
The fundamental theorem of calculus and definite integralsGet 3 of 4 questions to level up!

Quiz 1

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Indefinite integrals: reverse power rule

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Reverse power rule
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Indefinite integrals: sums & multiples
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Rewriting before integrating
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Reverse power rule review
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Practice
Reverse power ruleGet 3 of 4 questions to level up!
Reverse power rule: negative and fractional powersGet 3 of 4 questions to level up!
Reverse power rule: sums & multiplesGet 3 of 4 questions to level up!
Reverse power rule: rewriting before integratingGet 3 of 4 questions to level up!

Indefinite integrals of sin(x), cos(x), eˣ, and 1/x

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Indefinite integral of 1/x
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Indefinite integrals of sin(x), cos(x), and eˣ
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Common integrals review
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Indefinite integrals: eˣ & 1/xGet 3 of 4 questions to level up!
Indefinite integrals: sin & cosGet 3 of 4 questions to level up!

Quiz 2

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Finding definite integrals

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Definite integrals: reverse power rule
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Definite integral of rational function
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Definite integral of radical function
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Definite integral of trig function
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Definite integral involving natural log
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Definite integral of piecewise function
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Definite integral of absolute value function
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Practice
Definite integrals: reverse power ruleGet 3 of 4 questions to level up!
Definite integrals: common functionsGet 3 of 4 questions to level up!
Definite integrals of piecewise functionsGet 3 of 4 questions to level up!

Quiz 3

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𝘶-substitution

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𝘶-substitution intro
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𝘶-substitution: multiplying by a constant
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𝘶-substitution: defining 𝘶
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𝘶-substitution: defining 𝘶 (more examples)
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𝘶-substitution
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𝘶-substitution: rational function
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𝘶-substitution: logarithmic function
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𝘶-substitution warmup
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𝘶-substitution: definite integrals
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𝘶-substitution with definite integrals
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𝘶-substitution: definite integral of exponential function
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Practice
𝘶-substitution: defining 𝘶Get 3 of 4 questions to level up!
𝘶-substitution: indefinite integralsGet 3 of 4 questions to level up!
𝘶-substitution: definite integralsGet 3 of 4 questions to level up!

Average value of a function

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Average value over a closed interval
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Calculating average value of function over interval
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Mean value theorem for integrals
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Average value of a functionGet 3 of 4 questions to level up!

Interpreting behavior of 𝑔 from graph of 𝑔'=ƒ

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Interpreting the behavior of accumulation functions
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Interpreting the behavior of accumulation functions
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Visually determining antiderivative
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Interpreting the behavior of accumulation functionsGet 3 of 4 questions to level up!

Quiz 4

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Optional videos

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Proof of fundamental theorem of calculus
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Intuition for second part of fundamental theorem of calculus
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Unit test

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About this unit

The antiderivative of a function ƒ is a function whose derivative is ƒ. To find antiderivatives of functions we apply the derivative rules in reverse. The fundamental theorem of calculus connects differential and integral calculus by showing that the definite integral of a function can be found using its antiderivative.