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VICMath MethodsQuick questions

Unit 4

Quick questions on Definite integration and the fundamental theorem: VCE Math Methods Unit 4

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 wrong antiderivative?
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Especially the 1k\frac{1}{k} factor for ekxe^{kx}, sin⁡(kx)\sin(kx), cos⁡(kx)\cos(kx). Forgetting it makes the answer off by a factor.
What is bracket discipline?
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F(b)−F(a)F(b) - F(a) where FF has multiple terms requires brackets around the substituted expressions. Without brackets, sign errors cascade.
What is q1?
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Evaluate ∫13(2x+1) dx\displaystyle\int_1^3 (2x + 1)\,dx. [2 marks]
What is q2?
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Evaluate ∫0πsin⁡x dx\displaystyle\int_0^{\pi} \sin x\,dx. [2 marks]
What is q3?
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Given ∫04f(x) dx=10\displaystyle\int_0^4 f(x)\,dx = 10 and ∫01f(x) dx=3\displaystyle\int_0^1 f(x)\,dx = 3, find ∫14f(x) dx\displaystyle\int_1^4 f(x)\,dx. [2 marks]

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