1. Approximately compute the value of the following integral, as accurately as possible, using the composite Trapezoidal rule with h =1. integral from 0 to 2 of (e^(-x) / (2-x)^(2/3))dx

Q: Use Simpson’s Rule with n = 4 to approximate ∫1  ex^2dx

A: The given function is continuous on the interval [0, 1], then using Simpson’s rule to find the…

Q: Evaluate the integral 2x dx x – 6 ILO fer th

A: SOLUTION-

Q: / 1 – x2 dx (c)

A: Given I = ∫1-x2x3dx    ......... (1) Integration by parts ∫u(x).v(x)dx = u(x)∫v(x)dx…

Q: how I calculate the definate integral 3x^2-e^2x(dx) on the interval ln3 to 0

A: To find the definite integral

Q: Evaluate the integrals ∫tanh 2x dx

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Q: 14 Find the integrals using integration by parts. Lx(x + 4) dr --2

A: Given that:(a) ∫x(x+4)2dx

Q: 18) Use two compositions of composite Simpson's method to estimate the integral Inx dx

A: The Simpson's rule can be used to calculate the integral approximation. The formula used in…

Q: 7. Evaluate the integral using integration by parts. S cos (5x)e 2* dx.

A: Given the integrationI=∫cos(5x)e2xdx

Q: 12)Use the Trapezoidal Rule to estimate the integral ₁√x² - 1 dx using 4 intervals. Round to the…

A: Solve the following

Q: 1 use this fact and the properties of integrals to evaluate dx =3 (7 – 6x2) dx. Given that

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Q: dx (1 – x3

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Q: Set up the integral for the arc lengthof the function,y=4/3x^3/2 for 2≤x≤6 if you integrate with…

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Q: Find the approximate value of integral from 0 to 10 1/√(x2+1)dx to 4 decimal places using Simpsons…

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Q: 2ea dx (ет — 1)2 1

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Q: 5 .Use the definition of the integral to evaluate | (2x - 3)dx

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Q: 3. Evaluate the integrals √tanh x sech² xdx

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Q: Use any method to evaluate the integrals ∫x cos3 x dx

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Q: fxVx+5 dx :

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Q: Compute integral below with the use of substitution. eð 1 -dx x In° x

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Q: Approximate the integral from 1 to -3 of e-x dx using four equal subintervals.

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Q: Find indefinite integral.

A: ∫5lnz+3z dz Put, 5lnz+3=t⇒5·1z+0=dtdz⇒1zdz=dt5

Q: Evaluate the integral * In 2 tanh 2x dx

A: We have to find Integral of given function.

Q: Evaluate the integrals using the substitution method of e8x dx

A: To evaluate the integral: ∫e8xdx Solution: Let substitute t=8x. Differentiating both sides, we get…

Q: 1. Evaluate the integral using integration by parts where possible. Z2 x In(8x)dx

A: we  have ∫12x*ln(8x) dx   we have to apply integration by parts ∫u v dx = u∫v dx −∫u' (∫v dx) dx…

Q: 4. Evaluate the following integral by first reversing the order of integration dx dy.

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Q: Vcosh² y – 1 dy

A: consider I=∫cosh2y-1 dy

Q: Approximate the integral from 3 to -3 of (2+x2) dx using five equal subintervals.

A: We have to divide -3 to 3 into five equal subintervals.Length from -3 to 3 is 3 - (-3) =6So length…

Q: When using Simpson's rule to approximate the integral In(x+1)dx, then the upper bound of the error…

A: Consider the given information. I=∫23lnx+1dx Let's take 1 for n for the error bound. Calculate the…

Q: .find the integral by Gamma fun y(-ny)5 dy

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Q: Find the indefinite integral. Solution in handwritten. 1. secy (tany - sec y ) dy

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Q: Calculate the integral of x(1+ 3x)° dx .

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Q: 1. Find the exact value of the iterated integral by changing the order of the integration: 8 2 1…

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Q: .2 32. 8x dx, x > 8 -

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Q: In xdx 3. The approximation of the integral when applying composite Simpson's rule with n=4 is

A: The integral function is ∫35ln x dx. The value of n is 4.

Q: S dy V1+9y2 3.

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Q: | (3x² + 4x + 1) dx

A: The power rule of integral is,

Q: 4. Evaluate the integral: In6 -2x + sinh 2x|dx e2x + e-2x

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Q: Estimate the following definite integrals using the Trapezoidal rule and Simpson's rule. Estimate…

A: Given integral is ∫13 2x-1 dx Take fx =2x-1 Number of steps = 4 Step size h = 3-14 =24=12=0.5 So, h…

Q: Evaluate the integrals using integration by parts. ∫ cos-1 (x/2) dx

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Q: Use Simpson’s Rule with n = 4 to approximate ∫1  ex^2dx 0   (integral from 0 to 1 of e^x^2 dx)

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Q: How many times do you need to integrate by parts to reduce ff(In x)° dx to an integral of In x? ·

A: Given integral is ∫1eln x6dx

Q: Evaluate the improper integral. x In6x dx 0.

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Q: Use Simpson’s Rule with n=4 to approximate the integral 8∫0√xdx.

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Q: + 3x dz. x2 + 1

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Q: 1. Use the table of integrals to integrate the followin a) S sin ) s in () dt

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Q: dx (5 x)3

A: This question is related to definite integral, we will use the Integration by substitution method to…

Q: In 2 tanh 2x dx

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Q: 1 dx. cosh x

A: Rewrite the integral and using substitution method, we calculate the given improper integral.

Q: Evaluate the indefinite integral: S (sec²x+ +) dx x2+4

A: We will solve the problem.

Q: 7 Evaluate the improper integral, if exists : dx (5 – x)3

A:

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.