Rules of Integration (Leaving Cert Applied Maths): Quizzes

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Rules of Integration
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What mathematical process does integration reverse?

Differentiation

Using the power rule, what is ∫x3 dx\int x^3 \, dx?

x44+c\frac{x^4}{4} + c

In the power rule for integration, what two steps must you follow?

Add 1 to power, then divide by new power

Why do we need the constant of integration cc?

Derivatives of constants are zero

When should you NOT include the constant of integration?

In definite integrals

What is ∫7 dx\int 7 \, dx?

7x+c7x + c

Before integrating 1x5\frac{1}{x^5}, how should you rewrite it?

x−5x^{-5}

What is ∫1x dx\int \frac{1}{x} \, dx?

ln⁡∣x∣+c\ln|x| + c

What is ∫1ax+b dx\int \frac{1}{ax+b} \, dx?

1aln⁡∣ax+b∣+c\frac{1}{a}\ln|ax+b| + c

What is ∫e5x dx\int e^{5x} \, dx?

15e5x+c\frac{1}{5}e^{5x} + c

What is ∫sin⁡(3x) dx\int \sin(3x) \, dx?

−13cos⁡(3x)+c-\frac{1}{3}\cos(3x) + c

In the Fundamental Theorem, ∫abf(x) dx\int_a^b f(x) \, dx equals what?

F(b)−F(a)F(b) - F(a)

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