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.) The integral from zero to π/2 of the cubed root of 2 + cos(x) dx,    n = 4

Q: + 4 dx, n = 4 4 Exact Trapezoidal Simpson's

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Q: 2.0 Hence, evaluste Se? cosz de to 3 decimal places. CoS I

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Q: Use (a) the Trapezoidal Rule, (b) the Midpoint Rule,and (c) Simpson’s Rule to approximate the given…

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Q: 3. A Estimate cos(z²) dz using a. the Trapezoidal Rule and b. the Midpoint Rule, each with n = 4.…

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Q: (d) Evaluate dx exactly and show that the result is (Hint: substitute x = 4 tan u.) 1+ x2 Then, find…

A: Trapezoidal rule  (h/2)[f(x_0)+2(f(x_1)+f(x_2)+...+f(x_(n-1))+f(x_n)]

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A: We use trapezoidal rule ,midpoint rule,simpson's rule to approximate the given integral

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Q: Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule to approximate the given integral…

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Q: Use n = 4 to approximate the value of the given integrals by the following methods: (a) the…

A: First find the width of integral by using the formula ∆x=b-an,where a=0,b=2 and n=4.…

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Q: Evaluate the integral. (Use C for the constant of integration.) 2 sin?(x) cos (x) dx

A: Let the given integral be y - y = ∫2sin2xcos3xdxy = 2∫sin2xcos3xdxy = 2∫sin2xcos2xcosxdxy =…

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Q: Use (a) the Trapezoidal Rule, (b) the Midpoint Rule,and (c) Simpson’s Rule to approximate the given…

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Q: Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule to approximate the given integral…

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A: Given integral, ∫sin3θ cos6θ dθ It can be written as =∫sin2θ sinθ cos6θ dθ=∫1-cos2θ sinθ cos6θ…

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Q: Use the Midpoint Rule with the given value of n to approximate the integral. Round the answer to…

A: The given integral is: ∫072sin(x) dx Let f(x) be the integrand. f(x)=sin x

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A: Consider the following equation: ∫0211+x6dx,   n=8 Here, fx=11+x6, a=0, b=2 The width of each…

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A: We will use substitution to solve the given integral.

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Q: 1. Use a definite integral to find the area under the curve y = 5 – 2x over the interval [-1,2], and…

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Q: Use (a) the Trapezoidal Rule, (b) the Midpoint Rule,and (c) Simpson’s Rule to approximate the given…

A: (a) the Trapezoidal Rule

Q: 2. Calculate the integral , sin(x²)dx by the Gauss quadrature with n+1 = 2 and 3 quadrature points.…

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Q: Use the Table of Integrals on Reference Pages 6–10 toevaluate the integral. integral     sin 2 x cos…

A: Evaluate: ∫ sin2x cos x lnsin xdx

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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: Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule to approximate the given integral…

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Q: Consider the definite integral cos(1 + √x) dx A) To estimate this integral accurate to four decimal…

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Q: Use the Midpoint Rule with the given value of n to approximate the integral. Round the answer to…

A: ∫0π22cos4xdx,  n=4Then ∆x=π2-04=π8The subintervals are 0,π8,π8,π4,π4,3π8,3π8,π2By midpoint…

Q: Use the Table of Integrals on Reference Pages 6–10 toevaluate the integral. integral e t  (sin a t -…

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Q: Use the Table of Integrals on Reference Pages 6–10 toevaluate the integral. integral    x sin (x  2…

A: Given integral is ∫ xsinx2cos3x2dx. Consider u = x2. dudx=x2'du=2xdxdx=du2x Substitute u = x2 and…

Q: Evaluate the integral. (Use C for the constant of integration.) cos a da sin a

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Q: Find the indicated midpoint rule approximation to the following integral from 2 to 3: 3sin(p1/3 x)…

A: Interval is from 2  to 3 n=6 subintervals △x=b-a2△x=3-22=12 Intervals are 2+12=136Add  12 till we…

Q: 2. Using the Simpson’s rule with N = 4, find as accurately as possible numerical value of following…

A: Given that the integral is ∫1∞e-x22dx and n=4. Now find  h=b-a2=∞-12=∞h=∞ The value of h is…

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Q: Evaluate the given integral using the substitution (or method) indicated. (Use C for the constant of…

A: The given integral is- I=∫5x+1-5dx Let 5x+1=t Differentiating w.r.t. x to both sides- 5=dtdxdx=dt5

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.