Use the trapezoidal rule with n= 5 to approximate 8x dx and use the fundamental theorem of calculus to find the exact value of the definite integral. The approximate value of the integral from the trapezoidal rule is. (Simplify your answer.)

Q: What is the value of the definite integral 4x – 3 -dæ? dx? 1² – I 2

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Q: Evaluate the integral. |sin° (x)cos“ (x)dx

A: In this question, the exponent of cos(x) is even i.e. 4, and the exponent of sin(x) is odd i.e 5,…

Q: Evaluate the integral. (Use C for the constant of integration.) 64 + e* dx

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Q: compute the value of f f(x) dx? If so, what rules would you use to calculate the value of this…

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Q: Evaluate the integral 8x2 dx J (æ – 3)(x + 2)² - Note: Use an upper-case "C" for the constant of…

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

A: The given integral is ∫sin2πxcos5πxdx. Let u=πx. Then dx=1πdu. Solve the given integral using the…

Q: Decide on what substitution to use, and then evaluate the given integral using a substitution. (Use…

A: ∫xe6x2-4dx

Q: Using an appropriate substitution, the integral x³ csc²(x¹) cot(x4) is equal to -dx

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Q: Evaluate the integral: |x cosh x² dx sinh x +C 2 x sinh x? +C sinh x? +C x² sinh 2x +C

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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)]

Q: Use the trapezoidal rule with n = 4 to approximate the value of each integral. Then find the exact…

A: Given, ∫01exex+4dx

Q: In the given equation as folows, approximate the definite integral using the Trapezoidal Rule and…

A: Given :            ∫23 2 1 + x2 dx

Q: (- + =) dx when evaluated is equal to 3Vx, 11 Find the value of a. The definite integral 12

A: Given problem:- Th value is given as  ∫49-xa+13xdx=-1112 The integration formula is expressed as…

Q: Evaluate the definite integral (2 + x) dx by first sketching the region and then using a geometric…

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Q: Use the trapezoidal rule with n = 4 to approximate the value of each integral. Then find the exact…

A: Given- ∫13lnxxdx To Use- The appropriate trapezoidal rule to approximate the value of above integral…

Q: Use Simpson's Rule to approximate the value of the definite integral 2x dx with n = 8. a. 16.9283 b.…

A: Simpson rule formula is: ∫082x4 dx≈∆x3f(x0+4f(x1)+2f(x2)+4f(x3)+...+f(xn))...(1) Here, ∆x=8-08=1,…

Q: use a geometry formula to find the exact value of the definite integral  4x dx on the interval [0,b]

A: The given function is 4x with the interval [0,b].

Q: (a) Use the trapezoidal rule to approximate the integral. | (4x° + 4) dx = - 1 (Round the final…

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Q: Use the rules for definite integration and Jc dx= c(b - a) to evaluate the integral Į 3 dx. 3 dx =|…

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Q: Evaluate the integral. •3 dx x4/x² + 3 NOTE: Enter the exact answer.

A: Explanation of the answer is as follows

Q: Evaluate the integral. C x² e* dx NOTE: Enter the exact answer.

A: As per guidelines we have to solve one question Please repost the other questions again

Q: Use the error formulas to find n such that the error in the approximation of the definite integral…

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Q: The definite integral (-+ dx when evaluated is equal to- 11 Find the value of a." 12 ... -8 1. 3.

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Q: Evaluate the definite integral. 4 ti + t?j| dt

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Q: valuate, numerically, the following integrals: b) Sor sinx dx by using Simpson's rule ( take n = 4 )

A: Given, f(x)= (sin x)/x b= π/2 a=0 n= 4

Q: Given the definite integral 2 -dx ,with h = 0.1 (x + 1)2 1.1 Find the error bound when using the…

A: NOTE: According to guideline answer of one method can be given, for other please ask in a different…

Q: Use the Substitution Rule to find the following indefiniteintegrals. Check your work by…

A: The given integral is ∫22x+13dx

Q: Evaluate the integral. (Use C for the constant of integration.) sin 70 de

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Q: Use the Trapezoidal Rule and Simpson’s Rule to approximate the value of the definite integral for…

A: Given  ∫02x2dx ,n=4 First evaluate the integral using Trapezoidal rule…

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

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Q: 2 Find the definite integral fo5 tan(x)dx using strips of width for the trapezium rule correct to…

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Q: Using an appropriate substitution, the integral f e cos(e* + 1) dx is equal to:

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Q: Use substitution to change the integral into one that can be evaluated by a formula from geometry,…

A: Solution; Consider the given integral: I = ∫1e525-(ln x)2xdx Substitute ln (x) = u du = 1xdxwhen x =…

Q: Evaluate V16-x² dx dx be? Explain Then, what would the value of the integral 1+V16-x 0.

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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: Use trigonometric substitution to find or evaluate the integral. (Use C for the constant of…

A: By using trigonometric substitution evaluate the given integral, ∫x38+x2dx Rewrite the given…

Q: Evaluate the integral. (Use C for the constant of integration.) 7 cos (a) da sin(æ)

A: Explanation of the answer is as follows

Q: . Evaluate the following. Use only the rules and techniques of integration presented in the module.…

A: As per guidelines we have to solve one question Please repost the other questions again

Q: valuate the integral using the Trigonometric Substitution metho x² (81-x²)3/²2 dx

A: Topic:- application of integration

Q: Decide on what substitution to use, and then evaluate the given integral using a substitution. (Use…

A: Consider the expression 3x2-2=u. The power rule of differentiation states that d dx(xp)=pxp-1, where…

Q: Evaluate the integral. (Use C for the constant of integration.) 2 cos (a) da sin(a)

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Q: The definite integral f dx is equal to e – Vē. What should the value of k be to make the statement…

A: To find: The value of k. Given: The value of ∫1ke1xx2dx is e-e. Concept used: The integration of…

Q: Find the following integral. Note that you can check your answer by differentiation. / (t+ 1)? t2 dt…

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Q: Find approximate value of the following integral by using the trapezoidal rul 10 " 10 sin(20x²)dx…

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Q: (a) Consider the integral dx. Why can't this integral be computed using the Fundamental Theorem of…

A: Solution for a: Given integral is ∫-111x2dx We can write the above equation as…

Q: If you were to use a substitution of u = 3x³ + 6 to evaluate the definite integral below, what would…

A: Given integral: ∫-144x23x3+64dx We have to use substitution u=3x3+6 to evaluate the new limit of the…

Q: çin fxa-lex®dx dx 3?

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Q: Evaluate the following integral. x2 dx V1- 144x x2 dx = V1-144x? (Type an exact answer. Use…

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Q: Evaluate the integral. (Use C for the constant of integration) (X^7)/(e^3-5x^8) dx

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