The diagram shows the curve with equation y = 10x^(1/2) - (5/2)x^(3/2) for x > 0. The curve meets the x-axis at the points (0, 0) and (4, 0). [Figure 5.1] Find the area of the shaded region.

Mark scheme

Marking points from the official mark scheme (May/June 2023). The mark or mark type is shown in brackets.

1. [B1] ∫(10x^(1/2) - (5/2)x^(3/2)) dx = [20/3 x^(3/2) - x^(5/2)] B1 for contents of each { } then ISW.
2. [M1] Using limit(s) correctly in an integrated expression (defined by one correct power). Minimum acceptable working is their (160/3 - 32).
3. [A1] 64/3 or 21.3[333...] Condone the presence of π for the first 3 marks. Condone using the limits the wrong way around for the M mark and if -21.3 is corrected to 21.3 allow the A mark. SC: if M0 scored SCB1 is available for correct final answer If ∫(10x^(1/2) - (5/2)x^(3/2)) dx = 21.3 and no integration seen B1 only.