Use the Runge-Kutta method with step sizes h = 0.1, to find
approximate values of the solution of
y' + (1/x)y = (7/x^2) + 3 , y(1) = 3/2 at x = 0.5 .
And compare it to thee approximate value of y = (7lnx)/x +
3x/2
Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule
to approximate the given integral with the specified value of n.
(Round your answers to six decimal places.)
2
1
6 ln(x)
1 + x
dx, n = 10
Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule
to approximate the given integral with the specified value of
n. (Round your answers to six decimal places.)
π/2
0
3
2 +
cos(x)
dx, n
= 4
(a) the Trapezoidal Rule
(b) the Midpoint Rule
(c) Simpson's Rule
Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule
to approximate the given integral with the specified value of
n. (Round your answers to six decimal places.)
4
0
ln(3 + ex) dx, n = 8
(a) the Trapezoidal Rule
(b) the Midpoint Rule
(c) Simpson's Rule
Use Simpson’s Rule with n = 4 to approximate the value of the
definite integral ∫4 0 e^(−x^2) dx. (upper is 4, lower is 0)
Compute the following integrals (you may need to use Integration
by Substitution):
(a) ∫ 1 −1 (2xe^x^2) dx (upper is 1, lower is -1)
(b) ∫ (((x^2) − 1)((x^3) − 3x)^4)dx
Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule
to approximate the given integral with the specified value of
n. (Round your answers to six decimal places.)
π/2
0
3
1 + cos(x)
dx, n = 4
Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule
to approximate the given integral with the specified value of n.
(Round your answers to six decimal places.) 5 2 cos(7x) x dx, n = 8
1 (a) the Trapezoidal Rule (b) the Midpoint Rule (c) Simpson's
Rule
Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule
to approximate the given integral with the specified value of n.
(Round your answers to six decimal places.) 2 0 e^x/ 1 + x^2 dx, n
= 10 (a) the Trapezoidal Rule (b) the Midpoint Rule (c) Simpson's
Rule
A study was conducted on a high-pressure inlet fogging method
for a gas turbine engine. Researchers considered two models.
Partial output is provided below.
Source
Df
SS
MS
F
Regression
5
148526859
29705372
94
Error
61
19370350
317547
Total
???
167897208
Source
Df
SS
MS
F
Regression
???
142586570
47528857
???
Error
63
25310639
401756
Total
???
167897208
Answer the following questions rounding off at the nearest
integer.
The number of observations collected for the study is equal
to
The...