Integration and applications of integration — Question 11
QCAA 2023, Paper 1 · 5 marks
Q11 · 2023 · Technology-freeSimple familiar5 marks
QUESTION 11 (5 marks)
Determine the following definite integrals.
a)∫011+x21dx [2 marks] b)∫0π/42sin2(x)dx [3 marks] WORKED SOLUTION
QCAA guide · typeset solution
5 marksANSWERa) 4π; b) 4π−21. Worked solution
a) ∫011+x21dx=[tan−1x]01=4π. b) Using 2sin2x=1−cos2x,
∫0π/42sin2xdx=[x−21sin2x]0π/4=4π−21. correctly uses required integration rule
[1 mark]calculates value of definite integral
[1 mark]correctly uses required trigonometric substitution
[1 mark]uses suitable integration rules
[1 mark]calculates value of definite integral
[1 mark]One QCAA sample method typeset for web; criterion wording is adapted from the official marking guide.
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