The left, right, trapezoidal, and midpoint rule approximations were used to estimate =f²r f(x) dx, where f is the function whose graph is shown. The estimates were 0.7818, 0.8679, 0.8631, and 0.9540, and the same number of subintervals were used in each case. y = f(x) (a) Which rule produced which estimate? L = R₁ = T₁ = M smaller value larger value (b) Between which two approximations does the true value of of f²f(x) f(x) dx lie?
The left, right, trapezoidal, and midpoint rule approximations were used to estimate =f²r f(x) dx, where f is the function whose graph is shown. The estimates were 0.7818, 0.8679, 0.8631, and 0.9540, and the same number of subintervals were used in each case. y = f(x) (a) Which rule produced which estimate? L = R₁ = T₁ = M smaller value larger value (b) Between which two approximations does the true value of of f²f(x) f(x) dx lie?
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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Transcribed Image Text:The left, right, trapezoidal, and midpoint rule approximations were used to estimate
same number of subintervals were used in each case.
n
Mn
(a) Which rule produced which estimate?
Ln
Rn
=
=
||
y
1 k
||
y = f(x)
smaller value
larger value
2
(b) Between which two approximations does the true value of
X
→
2
#f²f(x
'2
[²₁
f(x) dx, where f is the function whose graph is shown. The estimates were 0.7818, 0.8679, 0.8631, and 0.9540, and the
f(x) dx lie?
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