Use a substitution (in the integral) to prove that L{f(at)} where L{f(t)} = F(s). %3D a

Q: Approximate the value of the integral by use of the trapezoidal rule, using n 8. 11 121-x dx

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Q: The integral Jo x°dx converges when a < 0 True False

A: Given integral is ∫0∞xαdx with α≤0 we check the value of integral for α≤0

Q: Evaluating the integral f In(r³)dx, where x > 0 yields:

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Q: O: If the improper integral converges,Show and find its valuo or ex plain why it diverges: O. X Sin…

A: The integral will converge if it is equal to some finite fixed value.

Q: | Va3+1 dx dy 0,

A: ∫01∫y1x3+1dxdy=∫01∫0x2x3+1dydx=∫01x3+1x2-0dx=∫01x2x3+1dx

Q: use the Comparison Test to determine whether or not the integral converges.

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Q: Evaluate the integral by making the given substitution. (Use C for the constant of integration.) -2x…

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Q: Evaluate the integral by reversing the order of integration. 16 dy dx y³ + 1

A: From the given problem, it is observed that the region of integration is x,y: x≤y≤4; 0≤x≤16. Draw…

Q: Express the integral in terms of the variable u, but do not evaluate it. e16 In x dx; = In x rel6 In…

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Q: dx

A: Given  The improper integral is ∫011xdx.   Formula :- Power rule of integration :- ∫xndx=xn+1n+1+c

Q: 61. dx dy 3y

A: the given double integral is: ∫01∫3y3ex2dxdy as we can notice that in the given double integral…

Q: Evaluate the integral by reversing the order of integration. 3 27 3ex* dx dy 3.

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Q: Evaluate the integral. (Use C for the constant of integration.) /1+√x ox dx

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Q: Evaluate the integral. (Use C for the constant of integration.) 2 dx ex/2

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Q: What does this integral converge to?

A: First calculate the corresponding indefinite integral

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

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

A: # As per the guidelines we are entitled to solve one question at a time, please resubmit the other…

Q: Approximate the following integral using the Trapezoidal rule: e+1 dx x In x and find a bound for…

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Q: b) Approximate the definite integral with Simpson's Rule and rn=4

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Q: Calculate the integral, if it converges. If it diverges, enter diverges for your answer. x'e dx

A: Given query is to find the value of integral and check it converges or diverges.

Q: Find the Integral. (Use C for the constant of Integration.) dx

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Q: dx x²+18

A: Given, I= ∫x²/√(x²+18) dx

Q: t e dr (1 – e")2

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Q: Evaluate the integral by making the given substitution. (Use C for the constant of integration. -6x…

A: We have to evaluate ∫e-6xdx ,   by substituting u=-6xWe have to evaluate ∫dt1-7t6 ,   by…

Q: 4. Use the comparison property to calculate if the following integral converge: sin? x dx. | 1+

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Q: sketch, reverse and evaluate the integral dy dz 15

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Q: Use the Trapezoidal Rule to approximate the integral of e^(3/x) dx from 2 to 3 with n=4 . Round the…

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Q: Evaluate the integral. ez dx

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Q: Use the Midpoint Rule with n = 6 to approximate the following integral to 3 decimal places In(x +…

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Q: Use substitution to find the indefinite integral

A: Given ∫1xlnxdx

Q: You want to use the trapezoid rule to approximate - x + 15 dx. How large must n be so that the…

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Q: Use the appropriate limits to determine if the following improper integrals converge or diverge. If…

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Q: Evaluate the following improper integrals. Tell whether it is convergent or divergent. dx (x-1)%

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Q: Evaluate the integral. (Use C for the constant of integration.) om | (In(x))? dx

A: To find: Rewriting the integral and applying integration by parts: Applying formula:

Q: Explain why the integral is improper and determine whether it diverges or converges. Evaluate the…

A: The given integral is:

Q: (a) f(x) dx =

A: -5

Q: Estimate the integral below by using Simpson's rule and Trapezoidal method with n=4, also find ET…

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Q: Determine if the improper integral converges and, if so, evaluate it. dx | 8+x Write F if the…

A: The improper integral given is- ∫0∞dx8+x To find whether it converges or not . If integral tends to…

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

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Q: S e'mx' dx Inx?

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Q: Use the appropriate limits to determine if the following improper integrals converge or diverge. If…

A: since u have asked multiple question in one task so we will be answering only first question.

Q: sketch, reverse and evaluate the integral dy dx

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Q: 1 dx : x2+25

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Q: Find the integral by using the appropriate formula. (Use C for the constant of integration.) In x dx

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Q: J. xinx) dx converges and evaluate the integral in those cases. Determine for what values of p the…

A: Consider the equation

Q: r8 2 dx dy

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Q: çin fxa-lex®dx dx 3?

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Q: Evaluate the improper integral, and whether it converges or diverges.

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Q: dx o (x–1)? 2.

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Q: 4. Evaluate this integral by reversing the order of integration: Vy3 +1 dy dx.

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