I. [15 marks] Apply ST/2(0, π/2) and ST/4(0, π/2) to sin x dx, 0 where Sh(a, b) is Simpson's rule...
(a) Estimate So sin(x + 1) dx by using either Simpson's Rule or Trapezoidal Rule with n= 6 (Round the answer to 6 decimal places). (b) Estimate the minimum number of subintervals needed to approximate the integrals with an error of magnitude less than 10-4 by the rule you used in part (a).
4. Consider using the Simpson's 1/3 rule to estimate the following integral I[cos(x 3)l dx (a) Find the approximate values of 1 when the step size h-: 2 and h 1 , respectively. (b) Find an upper bound of the step size h in order to guarantee that the absolute error (in absolute value) of the estimate is less than 0.001. Hint: 2 sin x cos x = sin (2x). I cos x I " The arguments of all trigonometric...
Q3/ Evaluate the following double integral by using Simpson's Rule Method 2 2 3xy) etx dx dy (x3 -2 0 Number interval 2 ? of (7 Marks)
Q3/ Evaluate the following double integral by using Simpson's Rule Method 2 2 3xy) etx dx dy (x3 -2 0 Number interval 2 ? of (7 Marks)
Consider the integral 8. eT dx Use Simpson's Rule with n = 6 to estimate the value of the integral. (a) (b) Your friend chose instead to estimate the integral above using the Midpoint Rule with n = 6, Noting that the second derivative: 4x2-4r +3)e z5/2 is an increasing function over the interval [1, 4], determine the maximum possible error in your friend's estimate
Consider the integral 8. eT dx Use Simpson's Rule with n = 6 to estimate...
10. Trapezoidal Rule is used to approximate the integral f(a) dx using 1- (yo +2y1 + 2y2 + x-na b-a + 2yn-1 +%),where Use this approximation technique to estimate the area under the curve y = sinx over。 a. π with n 4 partitions. x A 0 B: @ Δy B-A b. The error formula for the trapezoidal rule is RSL (12ba)1 where cischosen on the interval [a, b] to maximize lf" (c)l. Use this to compute the error bound...
(10 marks) Evaluate the integral [*r'e ce-dx; 1. Using Composite Trapezoidal rule with (n=4) 2. Estimate the error for the approximation in (a) 3. Using Composite 1/3 Simpson's Rule (n = 4).
just need help on question 4, question 3 is done
Vidx. 3-(a) Use Simpson's Rule with n 4 subintervals to estimate (b) Compute the integral exactly 4 For the integral of problem #3: (a) Use the Error Bound to find the bound for the error (b) Compute the error made when using this estimate. 2 AX- 3. (a) S니 J dx C3,S.9 Δx AX3 f)fx 2tx)x u A 3 AXn 322 42 X n 333 512 1시 2 X x...
upson's Rule with n=4 #5 (9) Use Simpson's Rule wi intervals to estimate ex-l at 16 Find the exact value - A the error. drant of the integral linpartas) and the =0: #5, Use integration by. Seť Int de #7 (a) Evaluate St sin x cos x dic (6) If g(x) = 5 Je tidt, find g'(x) and g'(o). |#8 use partial fractions to find substitution to evaluate $3x(x-3) dx #0 (a). Find 52 sin o do (6) Find the...
Paragraph Styles Voce Sraut Simpson's 1/3rd rule is an extension of Trapezoidal rule where the integrand is approximated by a second order polynomial instead of a first order polynomial. For a given function f(x) the integral of f(x) over an interval [a, b] using Simpson's 1/3rd rule is given by: S f(x)dx = odx =“ $(x)+4 ()+2 Ž f(x)+F(*,) a 1=1,3,5.... 1=2,4,6,... Where, n is the number of subintervals and h is the width of each subinterval. Write a complete...
W60. Compute (sin x + cos x)(4 – 2 sin 2x – sin? 2x)e" dx sin 2x where = 6 (0,7) Mihály Be Pirkulyiev Rovsen W38. Let (an)n be a sequence, given by the recurrence: man+1 + (m - 2) an an-1 = 0 where me R is a parameter and the first two terms of (an), are fixed known real numbers. Find me R, so that lim an = 0 n-00 Tad