Integration — Question 46
Original QCE Vault practice · 4 marks
Q46 · Practice questionComplex familiar4 marks
QUESTION 46 (4 marks)
Evaluate exactly ∫0π/2sin2xcos2xdx. WORKED SOLUTION
Practice marking scheme
4 marksWorked solution
Using sin2x=2sinxcosx and the half-angle identity, sin2xcos2x=41sin22x=81(1−cos4x). Hence ∫0π/2sin2xcos2xdx=[8x−32sin4x]0π/2=16π. Applies the double-angle identities.
[2 marks]Obtains the exact result.
[1 mark]Practice question aligned to the current QCAA syllabus; review the worked solution and marking criteria.
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