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

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Integrating Powers of x
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What is the general rule for integrating xnx^n?

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 ∫1x dx\int \frac{1}{x} \, dx equal to?

ln⁡∣x∣+C\ln|x| + C

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

It involves division by zero

What does CC represent in the integral ∫xn dx=xn+1n+1+C\int x^n \, dx = \frac{x^{n+1}}{n+1} + C?

Constant of integration

What are the two steps for integration?

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 dx\int 5\sqrt{x} \, dx (without the constant term)?

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

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