If m < f(x) < M for a < x < b, where m is the absolute minim m(b – a) < f(x) dx s M(ь — а). Use this property to estimate the value of the integral. 16 7Vx dx

Q: a) Evaluate the following integrals »f xe*dx 2) fx* sinx dx 3) x sin 2x dx

A: According to the guidelines of company I can only answer first three subparts of the question. For…

Q: Use the Simpson's Rule to evaluate the integral fx sin(x)dx. W/H N/" N /H 02/ O

A: We have to evaluate the integral ∫0πxsinxdx. Here, a=0 and b=π Let n=2 Hence, Δx=b−an=π−02=π2.…

Q: Q6 // Using the Simpson's rule for multiple integrals, evaluate the following integral; I Vx + y) dx…

A: The given integral is:

Q: Consider the functions given.evaluate the integrals

A: First we try to write the given function using the mentioned functions.

Q: B- Evaluate the integral 1-x (3-x-y dz dy dx /1-x²

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

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

Q: For what value of c does the integral converge? Evaluate the integral for this value of c.

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Q: 8x Evaluate the given integral Jo (4+x²)2 dx using the substitution u = 4 + x². A. Estimate to three…

A: topic - definite integration

Q: (a) The Composite Trapezoidal Rule applied to the integral - [ f(z)dx I = gives the error b - a, 4h³…

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Q: evaluate the given integral. Given L f (x)dx = 3 and L g(x)dx = -1, find  L (2f (x) - 3g(x))dx.

A: Consider: ∫fx dx=3 and ∫gx dx=-1  Evaluate: ∫2fx-3gx dx   Apply integration law: ∫af±bg=a∫f±b∫g,…

Q: The integral J dx reduces to e+1 where u = f(x) and for some constant k.Compute f(1).

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Q: Q7. Using Simpson's Rule evaluate the integral √² √1+xª dx using 8 subintervals.

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Q: 1. Evaluate the improper integral or show that it diverges. (a)/ e* dx 8. (b) / dx (c) d.r (d) /…

A: If the limit exists and is a finite number , we say that the improper integral converges .If the…

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

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Q: 1. Find the integral of f xe¯*dx using Trapezoidal with Romberg with k = 3.

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Q: Consider the integral 3 4х f (x, y) dy dx 0, Evaluate the integral for f (x, y) = 5x²y

A: Given Data: Integrand: ∫03∫04xfx, ydydx Function: fx, y=5x2y3 Integrate the function. ∫03∫04xfx,…

Q: To evaluate the integral f(x)dx, the substitution u= g(x) is used. Thus if g(x)= e* then dx =

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Q: Find an antiderivative f(x) for x) in 14. Then compute the definite integral fox) dx = f(1) - f(0).…

A: For the solution follow the next step.

Q: The integral dx reduces to f(x) and for some constant k. Compute f(1). where u %3D e*+1

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Q: Evaluate 19191 x2 dx 1)3 3 Estimate the integral with n = 8, use (A) Trapezoidal Rule (B) Simpson's…

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Q: The improper integral (A) e B) © ⒸO D 1 8 Stoe ex dx is

A: Given that,

Q: Demonstrate that for the function of the type va? + x2 you use the substitution X-atane and use it…

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Q: (b) Suppose f(t) = rect(t) and g(t) = u(-t). Using the convolution integral, derive an expression…

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Q: 3. Decide if the following improper integrals converge or diverge. dx (a) x2 + 4 (b) . xe" dx da (c)…

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Q: S. e* dx

A: Given: The integral is  ∫0+∞e-xdx   To determine: The value of the integral ∫0+∞e-xdx

Q: つe1ret×フとx1u1日 X72 Xとt、X valuate he integral 2)

A: ∫-x+2x2+2xdx

Q: 2. Approximate the following integrals using Gaussian quadrature with n = 1 and n = 2. 1 а) -dx x² –…

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Q: Using the Simpson's rule for multiple integrals, evaluate the following integral; V(x + y) dx dy

A: The Simpson's rule is given by the formula ∫abfxdx ≈Δ x3fx0+4fx1+2fx2+4fx3+…+4fxn-2+fxn-1. Here, a…

Q: If m s f(x) s M for a sxsb, where m is the absolute minimum and M is the absolute maximum of f on…

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Q: Using the trapezoid rule and 1 rectangle, the integral fo dx is approximated by This is an • because…

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Q: r3 0 d.x 16+ x²

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Q: Use the following property of the definite integral to estimate the definite integral: f/4 π/6 […

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Q: x* +7 dx x° +3x? 3 4 5 1 dx x´ +7 1 x+7 dx V3x° +x³ 3 S. 8.

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Q: (b) Consider the integral I = So f(x)dx for the function 1 f(x) = -2e-* + 4 2x 120 Approximate I…

A:

Q: If f is continuous from the integral 0 to 9 of f(x) dx = 20. find the integral 0 to 3 of x f(x^2)…

A: Given. ∫09f(x) dx=20 To determine. ∫03xf(x2)dx Let x2=u Differentiate the function x2=u.…

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: (b) Consider the integral I = f f (x)dx for the function f(x) = -2e + 4 1 x' +2x 120 Approximate I…

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Q: 6 r5 So f5x dy dx X 1

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

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Q: 1. Use the trapezoid rule to approximate the following integrals: (using n = 4 subintervals) a. (x³…

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Q: B) Use the following values to calculate the integrals: f(x)dx =5 and g(x)dx=12 5 a) [(f(x)+g(x))dx…

A: Given that∫05f(x)dx=5and ∫05g(x)dx=12

Q: 2. Approximate the following integrals using Gaussian quadrature with n = 1 and n = 2. 1 1 2 -dx 4…

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Find any value of c for which the improper integral cx + 36 x2 + 1 9. da x (4 x + 5) converges.

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Q: Approximate the integral fe* cos xdx using the composite Trapezoidal rule with M=5 subintervals. M-1…

A: The given integral is ∫01excos xdx. Approximate the integral ∫01excos xdx using the composite…

Q: 1 dx. x+ v1+x

A:

Q: For what values of  a is ∫0∞ eax cos x dx convergent? Evaluatethe integral for those values of a?

A: ∫0∞eaxcosx dx Now, ∫0∞eaxcosx dx=limt→∞∫0teaxcosx dx=limt→∞eaxa2+1acosx+sinx0t    ∵∫eaxcosbx…

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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Q: If f(z)dz = f(x)dæ + f(x)dx 7 what are the bounds of integration for the first integral? a = and b =

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Q: The upper bound of the error when using Trapezoidal rule to approximate the integral 5 S xe*dx is хе…

A: The given integral is,∫25xe-x dx

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