In(2x + 2) · dx a) Use Trapezoidal rule with n=4 to approximate the integration b) Estimate the error associated with the approximation c) How many subintervals (no. of n) needed to achieve error less than 10-2

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Q: 1- Use trapezium's Rule with n = 4 to approximate the integral Vx dx

A: We have to use formula of Trapezoid Rule.

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A: Given that: *∫sin-1u×du=u×sin-1u+1-u2+C The given expression is, ∫x×sin-1x2×dx Let,  x2=u,…

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Q: How large should n be to guarantee that the Trapezoidal Rule approximation to 8 203 – 96a? - lx - 2)…

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A: The Simpson's 3/8 rule states,∫ydx=3h8y0+2y3+y6+ . . . + yn-3+3y1+y2+y4+y5+ . . . +yn-2+yn-1+ynWe…

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Q: 25. By considering integration round a suitable rectangular contour, show that cosh ar dx cosh nx dx…

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Q: 3. Determine the number of sub-intervals required to approximate 3 -x² dx e using the Trapezoid Rule…

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Q: 1- Estimate the minimum number of subintervals needed to approximate the integral with an error of…

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Q: 2 By using Trapezoidal rule, the value of "h" in evaluating - 2x + 6)dx , by taking 10 subintervals…

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Q: 10. Prove by using integration by change in variable the ff. integral: dx du = arcsec x + C xVx2 - 1

A: To show∫dxxx2-1=sec-1x+C.

Q: 15 By using the substitution u = In x, evaluate In x dx up to five decimal places. In x If - dx is…

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Q: . Find the polynominal of degree 9 centered at 0 that best approximates f(x) =ln(x3+5) b. Now use…

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Q: 6. Find the midpoint and trapezoid rule approximations to sin Txdx using n=25 subintervals. 3

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Q: Q3: Use integration by parts (Tabular method) to find the integral (2³_2 x² + 3x +1) sin(2x) dr

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Q: dx = arcsec x + C xVx2 – 1

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A: =∫(x2+4)cos(x)dx Integrate by parts: ∫fg′=fg−∫f′g f =x^2+4, g′ =cos(x)   ↓ steps   ↓ steps f′…

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Q: Use the trapezoidal rule with n=6 subintervals to approximate the integral 1 to 4  ln(x+sqrt(x)) dx.

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A: The given integral is: ∫45∫23xcosydydx Here  x0=4, x1=5y0=2, y1=3fx,y=xcosy By Trapezoidal rule,…

Numerical Integration

In a mathematical investigation, numerical integration comprises a wide group of calculations for computing the mathematical estimation of definite integral, and likewise, the term is moreover in some cases used to depict the numerical solution of differential equations. The most important aspect of this theory is error analysis.