Integrating Powers of x (Edexcel A-Level Mathematics): Quizzes

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Integrating Powers of x
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What is ∫xn dx\int x^n \, dx for n≠−1n \neq -1?

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

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

n=−1n = -1

What is ∫x−1 dx\int x^{-1} \, dx?

ln⁡∣x∣+C\ln|x| + C

Calculate ∫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

Why is the constant CC included in indefinite integrals?

Indefinite integrals represent family

What are the steps to integrate xnx^n?

Add 1 to power, divide by new power

Calculate ∫14x2 dx\int_1^4 x^2 \, dx.

2121

What is ∫1x4 dx\int \frac{1}{x^4} \, dx?

−13x3+C-\frac{1}{3x^3} + C

What process does integration reverse?

Differentiation

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