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VICMath MethodsQuick questions

Unit 4

Quick questions on Antidifferentiation and indefinite integrals: VCE Math Methods Unit 4

4short 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 wrong sign on cos⁡\cos antiderivative?
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∫cos⁡(x) dx=sin⁡(x)+c\int \cos(x) \, dx = \sin(x) + c (no negative). ∫sin⁡(x) dx=−cos⁡(x)+c\int \sin(x) \, dx = -\cos(x) + c (negative).
What is q1?
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Find ∫(6x2−e3x) dx\displaystyle\int (6x^2 - e^{3x})\,dx. [2 marks]
What is q2?
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Find ∫(2x+sin⁡(4x))dx\displaystyle\int \left(\frac{2}{x} + \sin(4x)\right)dx. [2 marks]
What is q3?
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Given f′(x)=4x+cos⁡xf'(x) = 4x + \cos x and f(0)=3f(0) = 3, find f(x)f(x). [3 marks]

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