Wow, that was pretty breezy! I solved it a bit differently. I rotated the whole figure 45 degrees, and put it on an x-y plane centered at the center of the figure. I then found a formula for the blue circle and for the quarter circle centered at the bottom of the (now) diamond. Those are: y = sqrt(25 - x^2) and y = sqrt(100 - x^2) - sqrt(50) I solved that system of equations to figure out where they cross (on the right), at x=5 sqrt(14)/4. Then I set up the integral to find the area between those two graphs over the range x=0 to x=5 sqrt(14)/4, which gives a quarter of the total blue area. Multiply by 4 to get 29.276. Sure, I plugged the integral into Wolfram Alpha, but if we're just looking for a numerical answer, that's good enough, right?
Gracias por estos videos, me hacen pensar y aprender. Thanks for these videos, they make me think and learn.
Thanks for your comment, glad you enjoy 😀
Wow, that was pretty breezy! I solved it a bit differently. I rotated the whole figure 45 degrees, and put it on an x-y plane centered at the center of the figure. I then found a formula for the blue circle and for the quarter circle centered at the bottom of the (now) diamond. Those are:
y = sqrt(25 - x^2) and y = sqrt(100 - x^2) - sqrt(50)
I solved that system of equations to figure out where they cross (on the right), at x=5 sqrt(14)/4.
Then I set up the integral to find the area between those two graphs over the range x=0 to x=5 sqrt(14)/4, which gives a quarter of the total blue area. Multiply by 4 to get 29.276.
Sure, I plugged the integral into Wolfram Alpha, but if we're just looking for a numerical answer, that's good enough, right?
Nice solution!! I’ll talk a bit slower next video 😀
@@mrtalbotmaths Haha awesome!