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QLDMath MethodsQuick questions

Unit 3: Further calculus and statistics

Quick questions on Antiderivatives and the Fundamental Theorem of Calculus (QCE Mathematical Methods Unit 3)

5short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.

What is linear inside argument?
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If the argument is linear (ax+bax + b), divide by the coefficient of xx.
What is the Riemann sum definition?
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The definite integral ∫abf(x) dx\int_a^b f(x) \, dx is defined as the limit of a Riemann sum:
What is properties of the definite integral?
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These properties speed up Paper 1 evaluation.
What is wrong division on linear inside argument?
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∫e2x dx=12e2x+C\int e^{2x} \, dx = \frac{1}{2} e^{2x} + C, not 2e2x2 e^{2x}. Divide by the coefficient, do not multiply.
What is sign error on ∫sin⁡x dx\int \sin x \, dx?
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The antiderivative is −cos⁡x-\cos x, mirroring ddxcos⁡x=−sin⁡x\frac{d}{dx} \cos x = -\sin x.

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