EasyMathematicsHigh School (11–12)Functions and Calculus › Application of IntegralsNumericalA-Level AP Board Exam IB

A wheelchair ramp has a side panel. Its top edge is the line y = x/2 + 2, with x and y in metres…

Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

A wheelchair ramp has a side panel. Its top edge is the line $y = \dfrac{x}{2} + 2$ , with $x$ and $y$ in metres, from $x = 2$ to $x = 8$ . The bottom edge of the panel is the $x$ -axis. Find the area of the panel with an integral. Then check it with the trapezium formula, by finding the heights of the panel at the two ends.

Need a reminder? The key ideaShow

Cut the region under $y = f(x)$ into $n$ strips of width $\Delta x = \dfrac{b - a}{n}$ . The sum of the strips tends to the area as $n$ grows, and the area is $\displaystyle\int_a^b f(x)\,dx = F(b) - F(a)$ for an antiderivative $F$ .

The worked solution

Have you tried it?

Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

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