Use the composite Simpson's 1/3 rule with step length h = 0.4 to %3D estimate I = [ S" In(2 +3/ã) 1+x² In(2+3/x) dx,

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Q: 4 Given the integral: Jo 1+x² dx. Evaluate using Romberg's method. Tolerance = Nx10-6

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Q: # 1) If V is the volume of a cube with edge length x and the cube expands as time passes, find dV/dt…

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Q: 2 S (x) + x³)dx = ? -1

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Q: Use the composite Simpson's 1/3 rule with step length h = 0.4 to estimate I = In(2 +3/x) -dx, 12…

A: To use the composite Sympsopns 1/3 rule with step length h=0.4.

Q: b. Find the value of V1- 0.162sin²x dx using Simpson's 1/3rd rule, taking 6 equal subintervals

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Q: e ax dx

A: 1. Let In=∫xneaxdx. Use the integration by parts formula ∫udv=uv-∫vdudxdx to evaluate the integral…

Q: e the composite Simpson's 1/3 rule with step length h = 0.4 to estimate In(2+3/x) dx. -dx, 1+x²

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Q: Evaluate the integral ,(1 – x – 4x3 + 2x5) dx c) Single application of Simpson's 1/3 rule d)…

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Q: (b) Evaluate 1 dx using Romberg's S. 1 + x2 hence obtain an approximate value of T.

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Q: Jse the composite Simpson's 1/3 rule with step length h = 0.4 to estimate In(2+3/x) 1, dx, 1+x2 I =

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Q: (a) Consider the task of approximating e-4=* dx using the Composite Trapezoidal rule. How large…

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Q: 47) Estimate the minimum number of subintervals needed to approximate the integral 2 S (7x4 - 1x)dx…

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Q: Substitute the values of f(x), a, and b in the Integral from the previous step, and find the average…

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Q: Q3) Approximate the integral e* cos x dx using the composite Trapezoidal rule with M=5 subintervals.

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Q: Determine how large the number a has to be so that 1 dx

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Q: 4. Use the comparison property to calculate if the following integral converge: sin? a dx. V1+x3

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Q: The approximation of x' e¯*dx by Simpson's Rule is O 0.162402 O 0.160603 O 0.160602 O None of these…

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Q: How large should n be to guarantee that the Simpson's Rule approximation to dx is accurate to within…

A: Given:  ∫017ex2dx             where f(x)=7ex2 and a=0 , b=1.

Q: | 17e dx is accurate to within 0.0001? How large should n be to guarantee that the Simpson's Rule…

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Q: 4. Use the comparison property to calculate if the following integral converge: sin? x dx. | 1+

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Q: Calculate the percent error of: |(1.2 - x)(1- e20(x-)( 20.1) dx a. Using rectangular method when…

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Q: Compute an approximation to the value of Le-x*dx a) using Simpson's Rule b) using Simpson's…

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Q: Use the composite Simpson's 1/3 rule with step length h = 0.4 to estimate In(2+3/x) -dx, 9• I = 1+x²

A: Given: I=∫26 ln(2+3x)1+x2dx

Q: valuate the following integral: x2 + 5x + 6 dx. J ( – 1) (x2 + 3) |-

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Q: For what value of a, b > 0 is the following integral convergent. dx . x°(1+x³)

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Q: How large should n be to guarantee that the Simpson's Rule approximation to 19e is accurate to…

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Q: Q8. Using 1/3 Simpson's rule with h = 0.1 estimate (x³ – 3x2 + 2).dx

A: Formula Used: Simpson's 1/3 Rule ∫y dx=h3(y0+yn)+2(y2+y4+ . . . )+4(y1+y3+y5+ . . . )

Q: 4. Compute dx S in two ways and verify that the answers agree.

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Q: Compute x² In a dx both analytically and numerically. Use trapezoidal, Simpson's 1/3, Simpson's 3/8…

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Q: Find the values of p for which each integral converges 2 dx а. x(In x}P 1 b. x(In x) 2 2 dx a. For…

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Q: Use the composite Simpson's 1/3 rule with step length h = 0.4 to estimate In(2 + 3/x) dx. 1+x² I =

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Q: Find the intenal of cor 0 (-1)^xn 8. ht3

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Q: The value of pi can be approximated by calculating the integral: 0 to 1 of (4/(1+x2)) dx Calculate…

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Q: Evaluate J by means of Simpson's rule with n = 2m=10 and h = 0.10 = [*exp(-x²) dx Answer in 4…

A: f(x)=exp(-x2)h=b-an=1-010=0.10 table for x and y values x 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1…

Q: Calculate the integral approximation S12 for 1 dx. x²+1 S12 =

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Q: Use the composite Simpson's 1/3 rule with step length h = 0.4 to estimate In(2+37) -dx, 1+x?

A: According to the fundamental theorem of calculus ∫x0xnf(x)dx=F(xn)-F(x0), where dFdx=f(x). The…

Q: Evaluate the integral               0∫3 (−0.5x5+3.9x4−8.1x3+2.7x2+5.9x+1.5)dx using  four-point…

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Q: b. Find the value of V1-0.162sin²x dx using Simpson's 1/3rd rule, taking 6 equal subintervals

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Q: Q2 ) Use the Simpson's rule with (n = 4) to estimate thef²n sinx dx . 2

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Q: Find a value of x such that is equal to (a) ln 5 and (b) 1.

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Q: 12) a) Use either the Trapezoid OR Midpoint Rule to estimate [ In(1+e* ) dx using at least four…

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Q: Find the following improper integrals and then state whether it converges or diverges. a) S," In…

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