The top edge of a garden wall is a curve…

Step 1. The strips. The heights at $x = 0, 1, 2, 3$ are $2$, $3$, $6$ and $11$ metres. Each strip has width $1$ metre, so the estimate is $2 + 3 + 6 + 11 = 22$ square metres.

Step 2. The integral. $\displaystyle\int_0^4 (x^2 + 2)\,dx = \left[\dfrac{x^3}{3} + 2x\right]_0^4 = \dfrac{64}{3} + 8 = \dfrac{88}{3} \approx 29.33$ square metres.

Step 3. The gap. $\dfrac{88}{3} - 22 = \dfrac{22}{3} \approx 7.33$ square metres.