The depth of a straight drainage channel is modelled by
d(x)=4−x2d(x)=4-x^2d(x)=4−x2, 0≤x≤20\leq x\leq20≤x≤2,
where x x\,x and d d\,d are measured in metres across half of the channel. Eight equal-width rectangles are used to bound the cross-sectional area under this curve.
Explain which endpoints give the upper rectangle sum.
Calculate lower and upper bounds for the cross-sectional area.
The channel is 10 m long and its cross-section is assumed constant. State corresponding bounds for the volume represented by the model.
8 exam-style questions on OCR (MEI) A Level Maths 1.10.7 Upper and lower bounds using rectangles (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.