Integrating with Trigonometric Identities (Edexcel A-Level Mathematics): Quizzes

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Integrating with Trigonometric Identities
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Which identity is equivalent to tan⁡2θ+1\tan^2 \theta + 1?

sec⁡2θ\sec^2 \theta

What is ∫tan⁡2θ dθ\int \tan^2 \theta \, d\theta?

tan⁡θ−θ+c\tan \theta - \theta + c

Which expression equals sin⁡2θ\sin 2\theta?

2sin⁡θcos⁡θ2\sin \theta \cos \theta

What is ∫sin⁡2x dx\int \sin^2 x \, dx?

12x−14sin⁡(2x)+c\frac{1}{2}x - \frac{1}{4}\sin(2x) + c

What is ∫cos⁡2x dx\int \cos^2 x \, dx?

12x+14sin⁡(2x)+c\frac{1}{2}x + \frac{1}{4}\sin(2x) + c

Which expression for cos⁡2θ\cos 2\theta uses only sin⁡2θ\sin^2 \theta?

1−2sin⁡2θ1 - 2\sin^2 \theta

What is ∫tan⁡θ dθ\int \tan \theta \, d\theta?

−ln⁡∣cos⁡θ∣+c-\ln |\cos \theta| + c

Rearranging cos⁡2x=1−2sin⁡2x\cos 2x = 1 - 2\sin^2 x, what does sin⁡2x\sin^2 x equal?

12−12cos⁡2x\frac{1}{2} - \frac{1}{2}\cos 2x

What is ∫tan⁡3x dx\int \tan^3 x \, dx?

13tan⁡3x−tan⁡x+x+c\frac{1}{3}\tan^3 x - \tan x + x + c

What is ∫cos⁡2(10x) dx\int \cos^2(10x) \, dx?

140sin⁡(20x)+12x+c\frac{1}{40}\sin(20x) + \frac{1}{2}x + c

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