2.2 Based on the Fundamental Theorem of Calculus, show in two statements what may be wrong with the following calculation: 3 73 1 1 = - 3 4 2 dx = -1 1

Q: Ex 3.5.1 Let a = 3 .5-7. 13 and b = 2 -* .5.7.11 - 13*. Show that a|b by finding an z such that b =…

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Q: Use Simpson's Rule to evaluate the following. n = 10 +3 1 dx J-3 1+x²

A: SOLUTION-

Q: 59. Show that for any number a > 1 -Ina In x dx + e dy = a In a,

A: Given: ∫1alnxdx+∫0lnaeydy=alna

Q: 1. Use the Fundamental Theorem of Calculus Part II to evaluate each of the following: 1 3 a) + 8*…

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Q: Calculate the given integral: S4 sec°(11x) dx

A: Given : ∫4sec611xdx

Q: Use the Fundamental Theorem of Calculus to evaluate the following definite integral. | (4x2 + 9) dx…

A: To find the value of definite integral using  fundamental theorem of calculus.

Q: Use the Fundamental Theorem of Calculus to evaluate the following definite integral. 8 3 dt t 1

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Q: 1.Evalu ate the following integral 1-Co(x) dx d 1-4

A: Following are the integrations.

Q: Evaluate the following integral. 2x +5 dx - 2 Le 2x+5 dx = (Type an exact answer.) - 2

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Q: Use the fundamental theorem of calculus part 2 to evaluate the integral: 3 S (2x² – 3x + 3) dæ -2…

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Q: The value of the definite integral [²3x²dx 3x² dx is Select one: 3 26 1 26 26 none of the others 26…

A: Solution is given below:

Q: 2. (a) | +4 Evaluate the integral. √2x + 1 dx

A: Taking substitution as 2x+1 = t

Q: 2 X+2| dx -3

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Q: Question 5 Calculate the integral: da 9- x2 0.

A: Given that,

Q: 11) Simplify the following with both versions of the Fundamental Theorem of Calculus: e2t dt dx…

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Q: Evaluate the following integral. 3 5 e dz dx dy -2 4 1

A: Calculation:

Q: Evaluate the following integral. 1/12 tan 3 4x dx 1/24

A: let the given integral be I I=∫π24π12tan34x dx

Q: Evaluate the following integral. 5 4x-3 -dx x+1 5 ' 4x - 3 | (Type an exact answer.) x+1

A: Given integral is ∫054x-3x+1dx

Q: x 3*dx Jo

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Q: 9. Compute the following: /е 1 1 (a) dax 1 x2 (b) Inx dx х

A: Part (a)-Given:

Q: Which of the following is equal to / (2° – 7x)*dx = __" (x6 - (æ6 – 7x)5 + C ... O (2 – 7)5 +C ... ©…

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Q: 1. Use the Fundamental Theorem of Calculus to evaluate the following (DO NO 5x -6x dx 1 | cos (x)--…

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Q: EVALUATE THE FOLLOWING: 1. S 5x2+13x dx х3+2х2-х-2 dx 2. S Vx2 –4x+1 after appropriate use of…

A: Given  1) The integration is I=∫5x2+13xx3+2x2-x-2dx

Q: In 8) * dx Integrate and evaluate the following

A: we have to integrate the following

Q: Evaluate the integral. 7/2 sin 8t sin 7t dt 16 O 31 O T5 3

A: the given integral is ∫0π2sin8t sin7t dt use the formula Sin C sin D= -cosC+D+cosC-D2 here C=8t and…

Q: 2 (b) S(2 + tan (0))do (c) S 2'(1 + 5')dt

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Q: 6. Use symmetry to evaluate the following integral. (6x* - 5) dx

A: Given: -

Q: 17 + sin w sin(1+ cos w)) dw 7-2w

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Q: Evaluate the following integral. 1 tan (√3x) 1 2 (3x)² +(3x)² - 13 0 MIN 3 dx

A: Here we have to find the integral

Q: 2. 36 +x* dx =)

A: We have to solve

Q: 2ху 3. y' = -x?

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Q: 3.53 dx Compute 3+9,2

A: I=∫013313+9x2dx=19∫01331x2+13dx=19∫01331x2+132dx Since, ∫1x2+a2dx=tan-1xa

Q: 16 9. Evaluate the integral 4 dx.

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Q: 3. 2 1 What is the value of the integral 7xyz² dxdydz ? 0.

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Q: 3 (1 + 2x - 4x³) dx

A: The given integral is ∫131+2x-4x3dx

Q: fxsin(x' +5)dx

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Q: (iv) sec" (3x) tan(3x)dx

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Q: The integral 2N | 6xe- dx can be done with the substitution u = and du = dx.

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Q: Solve the folkowing di fferential equotions 1. xdy dx + dy x'

A: Firstly , we can solve for dydx. After that we can see that the equation is an homogeneous…

Q: (e 2x -1)2 dx 1. e 2x

A: A detailed solution is given below

Q: 11. The integral of tan(In|4x²|) dx is bln|sec(ln(2x)ª)|. What is b? А. 2 В. 1 D. ! С.4 4

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Q: The triple integral ¹³(12xze²y²) dxdydz is equal to 3(e − 1) - True False O

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Q: Evaluate the following integral. Question 16 dx 7- Vx 9.

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Q: 5. 4y°(x² + 4)- dy + 4xy = (x* + 4)² dx

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Q: ds 51. = 12r (3r - 1)', s (1) = 3 dt

A: As per our guidelines we are supposed to answer only one question. Kindly repost other question as…

Q: Evaluate the integral. 3-/4 5 sec e tan e de

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Q: 430 CHAPTER 5 Integrals 32. sin(In x) dx

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Q: 1. Evaluate the integral. -1 (6х — 12) dx

A: To evaluate the given integral.∫3-16x-12 dx

Q: 5. Calculate the integral f sin"( 1) cos'( t) dt, Your solution will be an expression in terms of m.…

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Q: 3. (Section 4.1) Evaluate each indefinite integral. (a) /202 (b) /(3e* + 2)dr 4x (c) / (182² + 6x +…

A: We have to solve in image