(a) Estimate the area under the graph of
f(x) = 4 + 2x2 from x = −1 to x = 2
using three rectangles and right endpoints.
R3 =
22

Correct: Your answer is correct.


Then improve your estimate by using six rectangles.
R6 =
19.75

Correct: Your answer is correct.


Sketch the curve and the approximating rectangles for R3.
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WebAssign Plot WebAssign Plot
Correct: Your answer is correct.

Sketch the curve and the approximating rectangles for R6.
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Correct: Your answer is correct.

(b) Repeat part (a) using left endpoints.
L3 =
16

Correct: Your answer is correct.
L6 =
16.75

Correct: Your answer is correct.

Sketch the curve and the approximating rectangles for L3.
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Correct: Your answer is correct.

Sketch the curve and the approximating rectangles for L6.
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Correct: Your answer is correct.

(c) Repeat part (a) using midpoints.
M3 =
M6 =

Sketch the curve and the approximating rectangles for M3.
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Correct: Your answer is correct.

Sketch the curve and the approximating rectangles for M6.
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WebAssign Plot WebAssign Plot
Correct: Your answer is correct.

(d) From your sketches in parts (a)-(c), which appears to be the best estimate?
M6
R6
L6