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VICMath MethodsQuick questions

Unit 2

Quick questions on Antidifferentiation introduction: VCE Math Methods Unit 2 Year 11

6short 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 initial value problem?
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Given f′(x)=…f'(x) = \ldots and a specific value f(a)=bf(a) = b:
What is power rule applied to 1/x1/x?
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The power rule for ∫xn dx\int x^n \, dx requires n≠−1n \neq -1. The antiderivative of 1/x1/x is ln⁡∣x∣\ln|x| (Unit 4).
What is antiderivative as plural?
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A function has infinitely many antiderivatives differing by a constant. The general antiderivative captures all of them via +C+ C.
What is q1?
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Find the general antiderivative of f′(x)=8x3−6x+5f'(x) = 8x^3 - 6x + 5. [2 marks]
What is q2?
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Given f′(x)=4x−3f'(x) = 4x - 3 and f(2)=1f(2) = 1, find f(x)f(x). [3 marks]
What is q3?
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A particle has velocity v(t)=3t2−4tv(t) = 3t^2 - 4t m/s and is at position x=5x = 5 m when t=0t = 0. Find x(t)x(t) and the position at t=2t = 2. [3 marks]

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