A-LevelMathematicsIntegration9709/33 · Oct/Nov 2022 · Q35 Marks
Find the exact value of ∫(from 0 to π/4) x sec²x dx.
- Find the exact value of ∫(from 0 to π/4) x sec²x dx.[5]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2022). The mark or mark type is shown in brackets.
- *M1 Commence integration by parts and reach x tan x - ∫ tan x .1 dx
- M1 Use a correct method to integrate tan x
- A1 Obtain integral x tan x - ln sec x , or equivalent
- DM1 Use limits correctly, having integrated twice
- A1 Obtain answer (1/4)π - (1/2)ln 2, or exact equivalent
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