A-LevelMathematicsIntegration9709/31 · Oct/Nov 2019 · Q68 Marks
COS X (i) By differentiating -, show that if y sin x 10 dy = - cosec²x. [2] = cot x then dy dx (ii) Show that 2 π ∫ x cosec²x dx = 4(π + 1n 4). [6] π
- (i)COS X By differentiating -, show that if y sin x dy = - cosec²x. dx = cot x then dy[2]
- (ii)2 π Show that ∫ x cosec²x dx = 4(π + 1n 4). π[6]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2019). The mark or mark type is shown in brackets.
- [M1] Use correct quotient rule
- [A1] Obtain dy/dx = -cosec²x correctly AG
- [*M1] Integrate by parts and reach axcot x + b ∫cot x dx
- [A1] Obtain -x cot x + ∫cot x dx OE
- [M1] State ±ln sin x as integral of cot x
- [A1] Obtain complete integral -x cot x + ln sin x OE
- [DM1] Use correct limits correctly
- [A1] Obtain (1/4)(π + ln 4) following full and exact working AG
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