a) Estimate the area under the graph of  f(x) = 7 + 4x2 from x = −1 to x = 2  using three rectangles and right endpoints. R3 = R6 = Sketch the curve and the approximating rectangles for R3 Sketch the curve and the approximating rectangles for R6.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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a) Estimate the area under the graph of 

f(x) = 7 + 4x2 from x = −1 to x = 2

 using three rectangles and right endpoints.

R3 =

R6 =

Sketch the curve and the approximating rectangles for R3

Sketch the curve and the approximating rectangles for R6.

(b) Repeat part (a) using left endpoints.

L3 =  
L6 =

Sketch the curve and the approximating rectangles for L3.


Sketch the curve and the approximating rectangles for L6.

(c) Repeat part (a) using midpoints.

M3 =  
M6 =

Sketch the curve and the approximating rectangles for M3.

Sketch the curve and the approximating rectangles for M6.

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

 

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