Use multiple application of simpson's 1/3 rule to numerically in- tegrate: f(x) = 8 + 5 sin (x) 0 to T from Use the intervals [0, T₂] . and [T/2, π]. your complete solution. • The estimate OF the integral For the first interval is I. = 17.5778. . For the second interval the esti- mate is 1₂ = 17.5778. Combining the two estimates, I 35.15554 with an error of D 0.5 1 1.5 2 2.5 0.065 2 Show 14 12 10 8 4 2 O 3 3.5
Use multiple application of simpson's 1/3 rule to numerically in- tegrate: f(x) = 8 + 5 sin (x) 0 to T from Use the intervals [0, T₂] . and [T/2, π]. your complete solution. • The estimate OF the integral For the first interval is I. = 17.5778. . For the second interval the esti- mate is 1₂ = 17.5778. Combining the two estimates, I 35.15554 with an error of D 0.5 1 1.5 2 2.5 0.065 2 Show 14 12 10 8 4 2 O 3 3.5
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.3: Euler's Method
Problem 7E: Use Eulers method to approximate the indicated function value to 3 decimal places, using h=0.1....
Related questions
Question
![formula:
→ f2(x)
(x-x₁)(x-X₂
(x - Xo) ( X-X2
Xi - Xo ) (X,-X2
f(x₁) +..
(Xo X₁) (Xo-Xz)
(x - Xo) ( x - X,)
[ Lagrange Method]
f (x₂)
(Xe - Xo) ( Xe-X)
where
the integral of second-order
interpolating polynomial, evaluated
from
Xo to X₂. X, is midway between Xo and the
- I = √f₂ (x)
f(x0) +](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdef63d31-f865-4b68-b515-a831fa63a48e%2F9c5cd6df-0f58-4563-87b7-75fad8fb512a%2F9o2kp28_processed.jpeg&w=3840&q=75)
Transcribed Image Text:formula:
→ f2(x)
(x-x₁)(x-X₂
(x - Xo) ( X-X2
Xi - Xo ) (X,-X2
f(x₁) +..
(Xo X₁) (Xo-Xz)
(x - Xo) ( x - X,)
[ Lagrange Method]
f (x₂)
(Xe - Xo) ( Xe-X)
where
the integral of second-order
interpolating polynomial, evaluated
from
Xo to X₂. X, is midway between Xo and the
- I = √f₂ (x)
f(x0) +
![use multiple application of simpson's 1/3 rule to numerically in-
tegrate:
f(x) = 8 +5 sin (x) from a to To
Use the intervals [0, T₂]
.
our Complete solution.
The estimate
OF
the integral For
the first interval is I₁ = 17.5778.
.
For the second interval the esti-
is 1₂ = 17.5778.
mate
.
Combining the
two estimates,
I 35.15554
with an
0 0.5 1 1.5 2
0.065 20
and [T/2, T ].
Show
14
12
10
8
4
2
O
2.5
3 3.5
error of](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdef63d31-f865-4b68-b515-a831fa63a48e%2F9c5cd6df-0f58-4563-87b7-75fad8fb512a%2Fgthgze_processed.jpeg&w=3840&q=75)
Transcribed Image Text:use multiple application of simpson's 1/3 rule to numerically in-
tegrate:
f(x) = 8 +5 sin (x) from a to To
Use the intervals [0, T₂]
.
our Complete solution.
The estimate
OF
the integral For
the first interval is I₁ = 17.5778.
.
For the second interval the esti-
is 1₂ = 17.5778.
mate
.
Combining the
two estimates,
I 35.15554
with an
0 0.5 1 1.5 2
0.065 20
and [T/2, T ].
Show
14
12
10
8
4
2
O
2.5
3 3.5
error of
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