Integrating Expressions (Leaving Cert Mathematics): Quizzes

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Integrating Expressions
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What is the general rule for ∫xn dx\int x^n \, dx when n≠−1n \neq -1?

xn+1n+1+C\frac{x^{n+1}}{n+1} + C

For which value of nn does the general integration rule NOT work?

n=−1n = -1

What is CC in the integration formula ∫xn dx=xn+1n+1+C\int x^n \, dx = \frac{x^{n+1}}{n+1} + C?

Constant of integration

What is ∫x−1 dx\int x^{-1} \, dx?

ln⁡∣x∣+C\ln|x| + C

Why doesn't xn+1n+1\frac{x^{n+1}}{n+1} work when n=−1n = -1?

It involves division by zero

What is an antiderivative?

Reversing the differentiation process

What are the two steps in the integration process?

Add 1 to power, divide by new power

What is ∫x2 dx\int x^2 \, dx?

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

What is ∫x−3 dx\int x^{-3} \, dx?

−12x2+C-\frac{1}{2x^2} + C

What is ∫14x2 dx\int_1^4 x^2 \, dx?

2121

What is ∫(5x+2) dx\int (5\sqrt{x} + 2) \, dx?

103x32+2x+c\frac{10}{3}x^{\frac{3}{2}} + 2x + c

How do you rewrite 1x4\frac{1}{x^4} for integration?

x−4x^{-4}

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