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Secure I https://www. aspx?homeworkld 413775268&questionld-3;&flushed; false&cld-4357542;&centerwin; yes Calculus 1 MATH1310, Section 204 Homework: Section 5.1 Score: 0.5 of 1 pt 3 of 5 (3 complete) HW Score: 30%, 1.5 of 5 pts 5.1.8 E Question Help using rectangles whose height is given the value of the function midpoint of the rectangle's base (the midpoint rue) estimate the area under the graph of the following function, using two and then four rectangles at the y 36 -x between 6 and 6 For two rectangles, area e an integer or a decimal.) Enter your answer in the answer box and then click Check Answer

Explanation / Answer

for 2 rectangle,

So midpoint rule given the function 36-x2 and for a 2 rectangles, therefore M2 is what we are solving for.

h = (6 - (-6))/2 = 6 <-sub sections

so values of x are -6,-4,-2,0,2,4,6.

But since we are doing the midpoint rule the midpoints are -5,-3,-1,1,3,5

so, so y values,

y=36-25=11

y=36-9=27

y=36-1=35

y=36-25=11

y=36-9=27

y=36-1=35

so area of 2 rectangle,

A= 1/2(11+27+35+35+27+11)

A=73

The area of 2 rectangle is 73.

for 4 rectangle,

So midpoint rule given the function 36-x2 and for a 4 rectangles, therefore M4 is what we are solving for.

h = (6 - (-6))/4 = 3 <-sub sections

so values of x are -6,-2,2,6

But since we are doing the midpoint rule the midpoints are -4,0,4

so the values of y are

y=36-16=20

y=36-0=36

y=36-16=20

so area of 4 rectangle,

A= 1/2(20+36+20)

A=38

The area of 4 rectangle is 38.

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