Edexcel IALMathematicsGeneral Applications10 Marks
Figure 1 shows a sketch of the curve with equation y = x² ln x, x>0. The curve has a minimum point M.
- (a)Find the exact coordinates of M.[5]
- (b)Find ∫ x² ln x dx.[3]
- (c)Hence find the exact area of the region bounded by the curve, the x-axis and the line x = e.[2]
This question uses a diagram from the original paper, which isn't shown here. Open the full paper from the past papers archive to see it.
Mark scheme
Marking points from the official mark scheme. The mark or mark type is shown in brackets.
- (a) M1: for attempting dy/dx using the product rule.
- (a) A1: for correct dy/dx.
- (a) M1: for setting dy/dx = 0 and solving for x.
- (a) A1: for correct x.
- (a) A1: for correct y.
- (b) M1: for attempting integration by parts.
- (b) A1: for correct first step.
- (b) A1: for correct integration.
- (c) M1: for using limits from 1 to e in their answer from (b).
- (c) A1: for correct exact area.
Write your answer and get it marked
On Oracle Prep you can write or photograph your own answer and have it marked by AI against this mark scheme, with feedback on what you missed.
Sign up free →