5.8 Trapezoidal ruleIB Maths: Applications and Interpretation HL: Mind map

Exam questions on 5.8 Trapezoidal rule

1. The surface of a lake is surveyed. Starting at one end, its width is measured every 20 m along its length. The six widths are 12 m, 30 m, 44 m, 50 m, 36 m and 8 m.
   The average depth of the lake is 2.5 m. Estimate the volume of water in the lake in m³.2 marks
2. Water flows into a tank at a rate of $R(t)=t^2+1$ litres per minute for $0\le t\le 4$, where $t$ is in minutes. The total volume of water that enters is the area under the graph of $R$.
   Use your GDC to find $\int_0^4 (t^2+1)\,dt$. Hence state whether the trapezoidal estimate is an over-estimate or an under-estimate, giving a reason.2 marks
3. A flower bed is bounded by the $x$-axis, the lines $x=1$ and $x=5$, and the curve $y=\sqrt{x}$, where $x$ and $y$ are in metres.
   Use the trapezoidal rule with 4 intervals of equal width to estimate the area of the flower bed.3 marks