1976 A-Level H2 Mathematics
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Question 7Techniques of Integration
Show that $\frac{\mathrm{d}}{\mathrm{d}\theta} \tan^3 \theta$ may be expressed as $3\tan^4 \theta + 3\sec^2 \theta - 3.$
Hence or otherwise, find $\displaystyle\int_{0}^{\frac{\pi}{4}} \tan^4 \theta \ \mathrm{d} \theta.$
Final Answer:
\(\dfrac\pi4-\dfrac23\)