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VICMath MethodsQuick questions
Unit 2
Quick questions on Antidifferentiation introduction: VCE Math Methods Unit 2 Year 11
9short 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 example 1. Simple polynomial?Show answer
$f'(x) = 3 x^2 - 2 x$. Antidifferentiate:
What is example 2. With initial condition?Show answer
$f'(x) = 4 x^3 + 6 x$ and $f(0) = 5$.
What is example 3. Kinematics application?Show answer
A particle has velocity $v(t) = 3 t^2 + 2$ m/s, and at $t = 0$ is at the origin. Find the position $x(t)$.
What is initial value problem?Show answer
Given $f'(x) = \ldots$ and a specific value $f(a) = b$:
What is forgetting $+ C$?Show answer
An indefinite integral without the constant of integration loses marks.
What is power rule applied to $1/x$?Show answer
The power rule for $\int x^n \, dx$ requires $n \neq -1$. The antiderivative of $1/x$ is $\ln|x|$ (Unit 4).
What is reversing the rule incorrectly?Show answer
Differentiate: multiply by $n$, decrease exponent. Antidifferentiate: increase exponent, divide by new exponent. The factor of $n$ goes opposite directions.
What is substituting before antidifferentiating?Show answer
When applying an initial condition, antidifferentiate the function first, then substitute.
What is antiderivative as plural?Show answer
A function has infinitely many antiderivatives differing by a constant. The general antiderivative captures all of them via $+ C$.