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QLDMath MethodsQuick questions
Unit 4: Further calculus and statistical inference
Quick questions on Integration of trigonometric functions: QCE Maths Methods Unit 4
10short 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 sign check?Show answer
The pattern for derivatives is:
What is example 1. Simple definite integral?Show answer
$\int_{0}^{\pi/4} \sec^2(x) \, dx = [\tan x]_{0}^{\pi/4} = \tan(\pi/4) - \tan(0) = 1 - 0 = 1$.
What is example 2. With reverse-chain factor?Show answer
$\int_{0}^{\pi/6} \cos(3x) \, dx = \left[ \frac{1}{3} \sin(3x) \right]_{0}^{\pi/6} = \frac{1}{3} \sin(\pi/2) - \frac{1}{3} \sin(0) = \frac{1}{3}(1) - 0 = \frac{1}{3}$.
What is example 3. Mixed integrand?Show answer
$\int_{0}^{\pi/2} [2 \sin x + \cos(2x)] \, dx$.
What is missing the $\frac{1}{k}$ factor?Show answer
$\int \sin(2x) \, dx = -\frac{1}{2} \cos(2x) + C$, not $-\cos(2x) + C$. This is the single most common error.
What is wrong sign on $\cos$ antiderivative?Show answer
$\int \sin x = -\cos x$ (sign change); $\int \cos x = +\sin x$ (no sign change).
What is using degrees instead of radians?Show answer
QCAA Methods Paper 1 uses radians. $\sin(\pi/2) = 1$; $\sin(90)$ in calculator mode-degrees is the same value, but the formula expects radians.
What is substituting $\pi$ as 3.14 in Paper 1?Show answer
Paper 1 expects exact values.
What is forgetting the constant of integration?Show answer
Indefinite integrals always include $C$. Definite integrals do not (it cancels in the subtraction).
What is sign-cancellation forgotten when integrand changes sign on the interval?Show answer
For total area, split at zeros and take absolute values; for signed integral, do not.