(1 – 3|x|) dx -2

Q: Evaluate J by means of trapezoidal rule using n = 10 and n = 20: 1 1 = [ exp(-x²)dx Note that this…

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Q: e2x sin 2x dx

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Q: Evaluate the following integrals using the appropriate technique. dx (a) S (b) Sp5lnp dp 5-3x

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Q: Approximate the following integrals using the Trapezoidal rule. 0.5 [h=24 dx x-4 a. [x² dx 10.5 b.

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Q: 6 (x²+1) dx S (23+3x-2)²

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Q: Approximate the following integrals using the Trapezoidal rule. r0.35 2 dx x2-4 1. 2. Sfx sin(x) dx…

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Q: Evaluate the following integrals dx V9 - x?

A: Given that, ∫x29 - x2 dx           ...(1) We can do this with trigonometric substitution. Consider,…

Q: 3 9-x 1 dy dx dz V9-2? (x² + y²)1/2 3

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Q: For the following integral: xe dx 1. Use the two-point Gauss quadrature approach to estimate the…

A: The given integral is :∫03xexdx The two point formula for gaussian approach is given by:…

Q: Q1 - Evaluate the following integrals i. Sxe-*dx

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Q: Evaluate the integral below using 2 point Gauss-quadrature and compare your results with the exact…

A: Given that, the integral is ∫15∫065y3+2x2+5dx dy. Note that, the formula for 2-point…

Q: (2+ v 9-x²) dx -3

A: Given integral is ∫-302+9-x2dx.

Q: Approximate the value of the given integral by use of the trapezoidal rule, using the given value of…

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Q: Use the trapezoid rule to approximate the following integrals: (using n = 4 subintervals) a.…

A: # As per the guidelines we are entitled to solve one question at a time, please resubmit the other…

Q: Use the Midpoint Rule to approximate the integral (7x + la?)dæ with n=3.

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Q: Evaluate the following by changing the order of integration: 5 sin(y*) dy dx. 5x

A: First we change the order of integration and find limit of integration.

Q: Use the substitution technique to determine the following integrals:

A: Important integrals for the question: ∫sec2 x dx = tan x + c ∫un du = un+1/(n+1) + c Other important…

Q: sin (x), dx b) J∞ 4+x²

A: Given improper integral: ∫-∞∞sinx4+x2dx Let x2=4tan2θ         x=2tanθdx=2sec2θdθ Substituting these…

Q: x-3 dx r³+9x +9.x

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Q: - dx 5x² +3 c)

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Q: Evaluate the following integrals S, 5v – 3) (e-y*2 sinhy) dy а. b. 8(x + 1) In(sinx2*) cosx dx

A: We have to define the given Delta function and find the points in which it is non zero in the given…

Q: Use Gauss-Legendre formula to evaluate the integral e¯x*dx_with n = 3.

A: Evaluate the integral          ∫01ex2dx using Gauss-Legendre formula with n=3.

Q: Q2) By using a division method. Evaluate the following integrals: y?tan-'ydy

A: To find the integration

Q: Estimate the integral below by using Simpson's rule and Trapezoidal method with n=D4, also find ET…

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Q: dx Vx²+2x+5

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Q: Approximate the following integrals using the Trapezoidal rule. 0.5 b. dx d. re dx

A: According to our guidelines we can answer only one question and rest can be reposted.

Q: T6 Based on the image attached, differentiate each of the following integrals with respect to x.

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Q: Q3 - Evaluate the following integrals dx x+V4x2+1

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Q: dx J 2 + Vx

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Q: Use reduction formula to evaluate the given integral xe" dx

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Q: Use the trapezoid rule to approximate the following integrals: (using n = 4 subintervals) a.…

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Q: Find the integrals below. a) |e2x dx b) S 3 dx

A: We have to find integrals of a)∫e2xdx b)∫3xdx

Q: Find formulas for the functions represented by the integrals.

A: Find formula for the function represented by the given integral: ∫1x2 t dt

Q: Q3 Evaluate the following integrals X. cosh? () dx -In2 1 - | 2 - cosh(lnx) dx

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Q: Use the substitution technique to determine the following integrals:

A: Let,

Q: Estimate the errors in the approximations for T10 and M10 of the integral from 1 to 2 of e1/x dx,…

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Q: 2. x² V1-x? dx_

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Q: Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's rule to approximate the integral 13 In(x)…

A: (1) The trapezoidal rule gives: So, T12≈2.0810

Q: The following integral can be evaluated only by reversing the order of integration: 2 dy dx. y5 + 1

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Q: 6 r5 So f5x dy dx X 1

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Q: Q3/ Find the integral x e* dx by using trapezoidal and simpson methods with an error of no more that…

A: According to question given :Integral ∫01x ex dx by using trapezoidal and simpson 38 methods with An…

Q: Use the trapezoid rule to approximate the following integrals: (using n = 4 subintervals) a.…

A: We have to find the integral using trapezoidal rule for n=4. I=∫02(2x3+3x2-1x)dx

Q: 16. | (ez/a – e-xla)dx. n/3 sec 0 tan 0 do. Vesec e 17.

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Q: find formulas for the functions represented by the integrals.

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Q: y V3 x dx 8y-y2

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Q: Approximate the following integral with n = 4 using trapezoidal rule. 2 dx |x|Vx² – 1 1.5

A: The trapezoidal rule uses trapezoids to approximate the area. The formula below is used to evaluate…

Q: Use the trapezoidal rule of integration to determine the value of the following integrals (a) (b) 2…

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Q: S, 3x²e* dx .2

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Q: 1 dx x2 (1) x=1 x=1 (2) et dx x=-0 x=-∞

A: (1) Consider

Q: 1. Approximate the following integrals using the Trapezoidal rule. c0.5 a. dx 1.5 x Inx dx c. 2x dx

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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.