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TASMath MethodsQuick questions

Unit 4

Quick questions on Antiderivatives of exponential and trigonometric functions (TCE Mathematics Methods, Tasmania)

1short 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 checking by differentiating back?
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The reliable way to confirm any antiderivative is to differentiate your answer and check you recover the original integrand. For instance, differentiating −13cos⁡(3x)-\tfrac{1}{3}\cos(3x) gives −13⋅(−3sin⁡(3x))=sin⁡(3x)-\tfrac{1}{3}\cdot(-3\sin(3x)) = \sin(3x), which confirms the antiderivative of sin⁡(3x)\sin(3x).

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