A-LevelMathematicsIntegration9709/23 · Oct/Nov 2017 · Q48 Marks
Find ∫ (4 + sin² θ) / (1 − sin² θ) dθ.
- (a)Find ∫ (4 + sin² θ) / (1 − sin² θ) dθ.[4]
- (b)Given that ∫(from 0 to a) (2 / (3x + 1)) dx = ln 16, find the value of the positive constant a.[4]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2017). The mark or mark type is shown in brackets.
- M1 (a) Obtain integrand of form a sec² θ + b
- A1 (a) Obtain correct 5sec² θ-1
- M1 (a) Integrate to obtain form a tan θ + bθ
- A1 (a) Obtain 5 tan θ – θ + c
- *M1 (b) Obtain integral of form kln(3x+1)
- A1 (b) Apply limits and obtain ⅔ ln(3a+1) = ln 16
- DM1 (b) Obtain equation with no presence of ln
- A1 (b) Obtain 21
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