Hi there!

Our interval is from 0 to 3, with 6 intervals. Thus:
3 ÷ 6 = 0.5, which is our width for each rectangle.
Since n = 6 and we are doing a right-riemann sum, the points we will be plugging in are:
0.5, 1, 1.5, 2, 2.5, 3
Evaluate:
(0.5 · f(0.5)) + (0.5 · f(1)) + (0.5 · f(1.5)) + (0.5 · f(2)) + (0.5 · f(2.5)) + (0.5 · f(3)) =
Simplify:
0.5( -2.75 + (-3) + (-.75) + 4 + 11.25 + 21) = 14.875
The formula for the radius r in terms of x . and for the maximum areas is x=2/
+4
Given that,
y forms a circle of radius r
y=2
r
r=y/2
(2-y)- forms Square Side x
(2-y) = 4x
x=(2-y)/4
Now Sum of Area's=Area of Square +Area of Circle
Sum =
r² + x²
Substitute the r and x values in above equation,
A(y)= y²/4
+(y-2)²/ 16
To maximize Area A(y)
A'(y)= 0
2y/4
+ 2(y-2)/16 =0
y/2
+ (y-2)/8 =0
y = 2
/
+4
Y max will be max, x to be maximum.
for maximum sum of areas,
x=2/
+4
Hence,The formula for the radius r in terms of x . and for the maximum areas is x=2/
+4
Learn more about Area :
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Hey guys it equals 12 alight