The figure above shows a unit square target for shooting on the rectangular coordinate plane. The target is divided into three regions 1, 2 and 3 by two curves as shown.
Find the area of the three regions.
Once again, this is a good moment to pause the article and give the problem a go yourself. When you’re ready, keep reading for the solution. And if you come up with your own approach, feel free to share it in the comments — I’d love to see how you tackled it.
Don’t forget to subscribe to our YouTube channel for more maths puzzles, it’s my goal to reach 100k subscribers someday.
Region 1
There are a couple of ways to solve for each region, but I will present you with the quickest and simplest method.
Notice that region 1 is bounded by the curve y = the square root of x, the line y = 1 and the y-axis. We will compute the area by considering integration along the y-axis.
Region 2
Region 2 is bounded by the curves y = the square root of x and y = x³. We can find its area by subtracting the top area from the bottom area.
Region 3
Region 3 is bounded by the curve y = x³, the line y = 1 and the x-axis. We can find its area as follows.
And that’s our answer. How amazing. Hey, don’t forget to clap👏 the article as a token of appreciation. Thank you 🦁
