QCEVault

Integration techniques — Question 217

Original QCE Vault practice · 5 marks

Q217 · Practice questionTechnology-freeComplex familiar5 marks

QUESTION 217 (5 marks)

Let I=∫01tan⁡−1x dxI=\int_0^1\tan^{-1}x\,dx, with angles in radians.
Arctan curve above its dashed endpoint chord pi*x/4 on [0,1].
a)
Determine I exactly using integration by parts.
[3 marks]
b)
Without decimals, show I>π/8I>\pi/8 using the curve shape.
[2 marks]
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