Derivative Rules + Riemann Sums + Integration Formulas + Summation Notation + Properties of the definite integral + FTC

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37 Terms

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(Derivative Rules) Product Rule

f(x)g’(x) + g(x)f’(x)

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(Derivative Rules) Quotient Rule

(g(x)f’(x) - f(x)g’(x))/g(x)²

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(Derivative Rules) Chain Rule

f’(g(x))g’(x)

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General Riemann Sums

A

<p>A <span>≈ </span></p>
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(Integration Formulas) ∫axcdx =

a · (xn+1)/(n+1) + c

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(Integration Formulas) ∫sin(ax)dx =

(-1/a) cos(ax) + c

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(Integration Formulas) ∫cos(ax)dx =

(1/a) sin(ax) + c

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(Integration Formulas) ∫sec(ax)tan(ax)dx =

(1/a) sec(ax) + c

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(Integration Formulas) ∫csc(ax)cot(ax)dx =

(-1/a) csc(ax) + c

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(Integration Formulas) ∫sec²(ax)dx =

(1/a) tan(ax) + c

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(Integration Formulas) ∫csc²(ax)dx =

(1/a) -cot(ax) + c

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(Integration Formulas) ∫(1/x)dx =

ln|x| + c

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(Integration Formulas) ∫eaxdx =

(1/a) eax + c

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(Integration Formulas) ∫baxdx =

(1/a ln b) bax + c

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(Integration Formulas) ∫1/(√1-(ax)²)dx =

(1/a) sin-1(ax) + c

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(Integration Formulas) ∫1/(1+(ax)²dx) =

(1/a) tan-1(ax) + c

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Definite Integral

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<p>(Summation Notation) Constant Value Rule</p>

(Summation Notation) Constant Value Rule

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<p>(Summation Notation)</p>

(Summation Notation)

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<p>(Summation Notation)</p>

(Summation Notation)

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<p>(Summation Notation)</p>

(Summation Notation)

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<p>(Summation Notation) Constant Multiple Rule</p>

(Summation Notation) Constant Multiple Rule

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<p>(Summation Notation) Sum/Difference Rule</p>

(Summation Notation) Sum/Difference Rule

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<p>(Property of Definite Integral) Constant Multiple</p>

(Property of Definite Integral) Constant Multiple

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<p>(Property of Definite Integral) Constant Multiple</p>

(Property of Definite Integral) Constant Multiple

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<p>(Property of Definite Integral) </p>

(Property of Definite Integral)

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<p>(Property of Definite Integral)</p>

(Property of Definite Integral)

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<p>(Property of Definite Integral)</p>

(Property of Definite Integral)

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<p>(Property of Definite Integral)</p>

(Property of Definite Integral)

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<p>(Property of Definite Integral)</p>

(Property of Definite Integral)

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<p>(Property of Definite Integral)</p>

(Property of Definite Integral)

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<p>(Property of Definite Integral)</p>

(Property of Definite Integral)

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<p>(Property of Definite Integral)</p>

(Property of Definite Integral)

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<p>(Property of Definite Integral)</p>

(Property of Definite Integral)

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<p>(FTC) </p>

(FTC)

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<p>(FTC)</p>

(FTC)

f(x)

(basically gives back original function)

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