Evaluate the following integral: • (a) analytically; • (b) single application of the trapezoidal rule; • (c) composite trapezoidal rule, with n = 2 and 4;

Q: Use the Special Integration Formulas to find the indefinite integral. ∫ (√9 + 4x2)

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Q: Evaluate the integral. (Use C for the constant of integration.) dx 81 - x2

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Q: Find the indefinite integral. (Use C for the constant of integration.) 8 cosh(Vx)

A: ∫8coshxxdxlet u=x,⇒ du=12xdx

Q: Evaluate the integral.  integral x2  sqrt (x+1)  dx

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Q: Use Simpson's rule to approximate the following integral and compare your 1. result to the exact…

A: The integral is given as

Q: (x²-x)dx

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Q: 1. Approximate the value of each of the following definite integrals using: i. Trapezoidal Rule

A: As per Bartleby's answering policy, we can answer only one question, so kindly post the remaining…

Q: Evaluate the indefinite integral: ∫ sec2(4x + 9) dx

A: Given: ∫sec2(4x+9) dx

Q: Identify the method applicable and evaluate the integral using the identified method: adx 5. S -…

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Q: Solve the definite integral using usub

A: To integrate,

Q: 2. Using both trapezoidal and Simpson rule, find the approximate values for the integral In(tan…

A: We need to find the approximate values of ∫π4π2ln(tan(x))dx using trapezoidal and Simpson rule given…

Q: Evaluate the following integrals using “Integration by Substitution”.

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Q: Evaluate the integral by using a substitution prior to integration /2s + 17

A: Here we have to evaluate,

Q: 2. Using both trapezoidal and Simpson rule, find the approximate values for the integral In(tan x)…

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Q: What's the difference between the Trapezoidal Rule and Simpon's Rule for approximating integrals?…

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Q: Evaluate the integral. (Use C for the constant of integration.)

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Q: Use the Trapezoidal Rule to evaluate the integral [x-'dx. .-1 1

A: Equation is f(x)=1xThe value of the table for x and y x 1 1.25 1.5 1.75 2 y 1 0.8 0.6667 0.5714…

Q: sin x dx 2 + cos² x

A: .............(1) substitute  put all values in equation 1

Q: Evaluate the integral. (Use C for the constant of integration.) 8x2 dx

A: Explanation of the solution is given below....

Q: (4-x²) dx

A: SOLUTION-

Q: use the trapeziodal and semson rule to approximate the following integrals

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Q: 15 Ső 0 X √x+1 ах

A: We have to solve the given definite integral

Q: Evaluate the definite integral using the Newton-Cotes quadrature formula (Trapezoidal Rule and…

A: According to the fundamental theorem of calculus ∫abf(x)dx=F(b)-F(a), where  dFdx=f(x). The 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: 4. fx√x - 3 dx

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Q: Evaluate the integral.  integral x2 /sqrt (x+1)  dx

A: Given I=∫x21+xdx

Q: Evaluate the integral. (Use C for the constant of integration.) 1- 36x2 dx

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Q: Evaluate the integral. (Use C for the constant of integration.) 9xV1- x4 dx

A: Formula used: ∫a2-x2dx=xa2-x22+a22sin-1xa+C Calculation: Simplify the integral as follows:…

Q: Evaluate the integral. (Use C for the constant of integration.) √3x√1- 3x√ 1 - x4 dx

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Q: Evaluate the integral. (Use C for the constant of integration.) 6x 6 dx

A: We have to solve integration by using exponential integral formula.

Q: Evaluate the integral. (Use C for the constant of integration.) 5xV1 - x4 dx

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Q: Evaluate the integral ( Use C for the constant integration) ∫ 11 tan4(x) sec6(x) dx

A: I=∫11tan4x×sec6x dx=11∫tan4x×sec4x×sec2x dx=11∫tan4x×1+tan2x2×sec2x dx                      ⋯⋯(1)

Q: 17 Evaluate the integral: SERV - dx x²√x² + 25 (A) Which trig substitution is correct for this…

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Q: Evaluate the integral. (Use C for the constant of integration.) 8x 8 dx 8x e

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Q: Evaluate the integral. (Use C for the constant of integration.) x2 - 64 dx

A: The given integral is ∫x2-64x3dx. Let us assume u=x2-64 and v'=1x3. Differentiate u with respect to…

Q: For Trig integration find the integral of  Sec^6(6x)

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Q: Evaluate the integral. (Use C for the constant of integration.) 7-6x - x² dx

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Q: 2. Use the composite trapezoidal rule to estimate the integral of y = sin(x) %3| from x = 0 to 2.…

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Q: Evaluate the integral. Use C for the constant of integration. 4dx

A: Given integral is- I=∫4dx9x3 It can be written as- I=49∫1x3dx=49∫1x32dx=49∫x-32dx

Q: Evaluate the integral. (Use C for the constant of integration.) 9 - x xp

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Q: Evaluate the integral. (Use C for the constant of integration.) 9)sin(xx) dx

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Q: Evaluate

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Q: Evaluate the integrals using the substitution method of sec2 (4x) dx

A: Given: Let I=∫sec24x dx To Find: To evaluate the given integration using substitution method

Q: In x dx .2

A: We need to solve the integral.

Q: use the trapeziodal and semson rule to

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Q: Use Property 8 of integrals to estimate the value of    ∫13 √ (x2  + 3 ) dx

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Q: 3.a) Apply the Trapezoid and corrected trapezoid rule, with h =, to approximate the integral…

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Q: Evaluate the integral. (Use C for the constant of integration.) 6x2 + 8x + 3) dx

A: ∫16x3-6x2+8x+3 dx

Q: Evaluate the definite integral. Axe dx 16204 Additional Materials eBook

A: We have to integrate