Consider the function f: [-1,3] → R defined by f(x) = x². A. Estimate the area between the graph of function f and the horizontal axis using an upper sum with four rectangles of equal width. horizontal axis using a right sum with eight
Consider the function f: [-1,3] → R defined by f(x) = x². A. Estimate the area between the graph of function f and the horizontal axis using an upper sum with four rectangles of equal width. horizontal axis using a right sum with eight
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Help with A
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3. Consider the function f : [-1, 3] → R defined by f(x) = x².
A. Estimate the area between the graph of function f and the horizontal axis using an upper sum with
four rectangles of equal width.
B. Estimate the area between the graph of function f and the horizontal axis using a right sum with eight
rectangles of equal width.
C. Estimate the area between the graph of function f and the horizontal axis using a lower sum with four
rectangles of equal width.
D. Estimate the area between the graph of function f and the horizontal axis using a left sum with eight
rectangles of equal width.
3/12 2 5/12 3
[(xi)
A = 7 D₂ H(₂)
?
A = AX (F(1₁) + f(1₂) +(1.3)
+ f(xx) + [(is) + f(x6] + [4₂]
+ flax)
A₁ = ² (0+ + + 1 + 2 +4 + 38 ) = 55/41 7/2) 58/6
+
3
A₁ = = ((0) + ( + ₁)) = 4+² = 2/6/² 2/7 (12) = 3/8
8
29/4
Area-
W.E.
MELT
Fheight
ܐ
Ax Faxi)
widach
B
fax)=x²
@ 100%
+:
ماد
area under
the curt
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Transcribed Image Text:me
سے
کرنے
کے
11
3:47 PM Mon Jan 30
4
5
Jurn
(D)
--+-1/2 P
42 1
T
d/6 td H
T
мене
3. Consider the function f : [-1, 3] → R defined by f(x) = x².
A. Estimate the area between the graph of function f and the horizontal axis using an upper sum with
four rectangles of equal width.
B. Estimate the area between the graph of function f and the horizontal axis using a right sum with eight
rectangles of equal width.
C. Estimate the area between the graph of function f and the horizontal axis using a lower sum with four
rectangles of equal width.
D. Estimate the area between the graph of function f and the horizontal axis using a left sum with eight
rectangles of equal width.
3/12 2 5/12 3
[(xi)
A = 7 D₂ H(₂)
?
A = AX (F(1₁) + f(1₂) +(1.3)
+ f(xx) + [(is) + f(x6] + [4₂]
+ flax)
A₁ = ² (0+ + + 1 + 2 +4 + 38 ) = 55/41 7/2) 58/6
+
3
A₁ = = ((0) + ( + ₁)) = 4+² = 2/6/² 2/7 (12) = 3/8
8
29/4
Area-
W.E.
MELT
Fheight
ܐ
Ax Faxi)
widach
B
fax)=x²
@ 100%
+:
ماد
area under
the curt
<
217
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