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1 Pure Mathematics

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Question 357

In this question x x\,x and θ \theta\,θ are measured in radians.

a.

Find ∫cos⁡x dx\displaystyle\int \cos x\,dx∫cosxdx.

[1]
b.

You may use the result ddx(tan⁡kx)=ksec⁡2kx\dfrac{d}{dx}(\tan kx) = k\sec^2 kxdxd​(tankx)=ksec2kx. Find ∫2sec⁡24x dx\displaystyle\int 2\sec^2 4x\,dx∫2sec24xdx.

[2]
c.

Hence, using the identity tan⁡2θ≡sec⁡2θ−1\tan^2\theta \equiv \sec^2\theta - 1tan2θ≡sec2θ−1, find ∫tan⁡2θ dθ\displaystyle\int \tan^2\theta\,d\theta∫tan2θdθ.

[2]
Markscheme

1 Pure Mathematics Questions

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