A-LevelMathematicsIntegration9709/33 · Oct/Nov 2021 · Q910 Marks
Let f(x) = 1 / ((9-x)√x)
- (a)Find the x-coordinate of the stationary point of the curve with equation y = f(x).[4]
- (b)Using the substitution u = √x, show that ∫ from 0 to 4 of f(x) dx = ½ ln 5.[6]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2021). The mark or mark type is shown in brackets.
- [M1] Use quotient or product rule
- [A1] Obtain correct derivative in any form
- [M1] Equate derivative to zero and solve for x
- [A1] Obtain answer x = 3
- [B1] State du/dx = 1/(2√x), or dx = 2√x du, or 2u du = dx
- [B1] Substitute and obtain integrand 2/(9−u²)
- [M1] Use given formula for the integral or integrate relevant partial fractions
- [A1 OF] Obtain integral 1/3 ln((3+u)/(3−u))
- [M1] Use limits u = 0 and u = 2 correctly
- [A1] Obtain the given answer correctly
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