The Basics (Leaving Cert Mathematics): Flashcards

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Integrating Expressions
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General rule: ∫xn dx\int x^n \, dx

xn+1n+1+C\frac{x^{n+1}}{n+1} + C for n≠−1n \neq -1

Value of nn where integration rule fails

n=−1n = -1

∫1x dx\int \frac{1}{x} \, dx

ln⁡∣x∣+C\ln|x| + C

Meaning of CC in indefinite integrals

Constant of integration

Integration is the reverse of

Differentiation

Differentiation steps with powers of xx

Multiply by power, subtract 1

Integration steps with powers of xx

Add 1 to power, divide by new power

∫x2 dx\int x^2 \, dx

x33+C\frac{x^3}{3} + C

∫x−3 dx\int x^{-3} \, dx

−12x2+C-\frac{1}{2x^2} + C

Rewrite 1x4\frac{1}{x^4} as a power of xx

x−4x^{-4}

Evaluating definite integrals

Find antiderivative, evaluate at limits, subtract

Why include +c+c in all integrations

Indefinite integrals represent a family of functions

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The Basics

Average Value of a Function

Area Under/Between Curves

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Average Value of a Function

Area Under/Between Curves

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The Basics

Average Value of a Function

Area Under/Between Curves

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The Basics

Average Value of a Function

Area Under/Between Curves

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