Answer:
D (2,-2)
Step-by-step explanation:
- The coordinates are the pair (x,y) in the axis.
- We already have three vertexs: a: (x,y)=(2,3); b:(x,y)= (7,3) and c: (x,y)=(7,-2).
- If you see the picture attached, where all points available are in pink, you will see that the distance between the sides that are already defined equals 5.
- Because all squares have equals sides, then we must find the missing side that will be at a distance of 5 between the other two vertexs.
- That point is d (x,y)=(2,-2).
Let F be the primitive of f, i.e.

Then, we have

So, we have
![\displaystyle \int_0^5(2x-2)\;dx = \left[x^2-2x\right]_0^5 = 25-10=15](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cint_0%5E5%282x-2%29%5C%3Bdx%20%3D%20%5Cleft%5Bx%5E2-2x%5Cright%5D_0%5E5%20%3D%2025-10%3D15)
As for the sine, we can spare the integral: the sine is an odd function, which means that it is symmetrical with respect to the origin. Any odd function integrated over a symmetrical neighborhood of zero (i.e. any interval of the form [-n,n]) returns zero: by symmetry, there is an equal amount of positive and negative area. So, we have

R equals 20 in this situation.