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

In the power rule for integration, what do you do to the power of xx?

Add 1 then divide by new power

Why must we add a constant of integration +c+c to indefinite integrals?

Derivative of any constant is zero

When integrating a definite integral, should you include the constant +c+c?

No, it gives a specific numerical value

What is ∫5x2dx\int 5x^2 dx?

5x33+c\frac{5x^3}{3} + c

What is ∫7dx\int 7 dx?

7x+c7x + c

Before integrating 1x4\frac{1}{x^4}, how should you rewrite it?

x−4x^{-4}

What is ∫1xdx\int \frac{1}{x} dx?

ln⁡∣x∣+c\ln|x| + c

What is ∫13x+5dx\int \frac{1}{3x+5} dx?

13ln⁡∣3x+5∣+c\frac{1}{3}\ln|3x+5| + c

What is ∫e4xdx\int e^{4x} dx?

14e4x+c\frac{1}{4}e^{4x} + c

What is ∫sin⁡(3x)dx\int \sin(3x) dx?

−13cos⁡(3x)+c-\frac{1}{3}\cos(3x) + c

In ∫abf(x)dx=F(b)−F(a)\int_a^b f(x) dx = F(b) - F(a), what is F(x)F(x)?

The antiderivative of f(x)f(x)

For definite integrals, which value do you subtract from which?

F(upper) minus F(lower)

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