In tan"u du where n is any integer, we use the transformation for tan²u= sin²u cos?u

Q: Question 11 Evaluate: (ed"+1) /Ted" + 1)?-4 3x A) None B sec -C sec D sec-1 +C E +C 2 Sec-

A: First we put e3x+1=t and differentiate both sides with respect to t and solve it.

Q: (x+1)dx If (x+2)(x– 1)² A B 2 + dx ,the values of A & C respectively are x - 1 (x- 1)² . 9 3 x+2 (A)…

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Q: () If h(x) = | cosxdx and h =4, then h (0) is equal to 4 A -3 B 3 4 D -4 E) None C.

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Q: dx dx is converted to: 4+Vx By algebraic substitution, the integral - 2ydy y+4 B y+4 © [ vdy y+4 dy…

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Q: By algebraic substitution, the integral - dx dx is converted to: 4+x 2ydy (A y+4

A: Option a is the correction and other option does not satisfy the given conditions

Q: The New River Gorge Bridge is 880 feet above the water below. A bottle rocket is launched upward off…

A: To find out the velocity and acceleration.

Q: Evaluate each of the following indefinite integrals: Show complete and detailed solutions. Express…

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Q: Evaluate this path limit: 4.xy3 =??? lim (x, y)¬(0, 0) 2x² +y6 x=y3

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Q: The region is bounded by the curve y = 6x – x² and y = x² – 2x –

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: dx dx is converted to: 4+Vx By algebraic substitution, the integral - 2ydy y+4 B y+4 © [ vdy y+4 dy…

A: Given, u= ∫dx/(4+√x) We can solve it by substitution method.

Q: dx Vx3 V2 + x

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Q: dx -dx is converted to: 4+Vx By algebraic substitution, the integral |- 2ydy A y+4 dy B y+4 ydy © S…

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Q: To evaluate y-csc²(y³) cor²(y³)dy, we let u =csc(y³) (A) True B) False

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Q: dx is 2/x – Sin|/x +s|+c. Vx +5 The antiderivativeof | - A True B) False

A: To find the antiderivative of the function

Q: Match the Integrals on the left side with the appropriate technique of integration to use on the…

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Q: Luse the Half Anola Forula cos2

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Q: To evaluate sin*2x cos 2x dx , the identities to be used is/are: sin4x, 1- cos4x A 2 B cos²2x=1-…

A: Solution:-  This types of trignometric integrals can be solve by reduction formula of integral.

Q: Which of the following is equal to sec 2 x tan³x dx to obtain the correct indef inite integral?

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Q: Determine the intervals on which the following function is concave up or concave down. Identify any…

A: The given function,  g(t)=3t5-20t4+30t3+80

Q: What’s the concepts of calculating the area of a region with subintervals of equal widths and…

A: The concept behind calculating the area of a region with subinterval of: a) Equal width- It is…

Q: 25 -x2 In -dx , if we let u =/ 25 – x2 , then udu = - xdx. (А) True B) False

A: We can solve as follows

Q: The data is known as follows: 7 4 5 P(x) | 48 | 100 294 900 | 1210 | 2028 10 | 11 13 Using Newton's…

A: We need to apply Newton's divide difference interpolation.

Q: Evaluate: Jevdx. A = 2ev/x+1)+C © - 2evã(/x+1) B + C © =2ev^(/x-1)+c

A: To solve the following integral

Q: 2х + 3, х<I f (x) dx if f(x) = Evaluate 5, A 21 B) 19 28 D 16

A: We will evaluate both the integrals as following.

Q: 1 6. cos-xdx cos* xdx xprt.

A: We need to solve the integral.

Q: de 6) S 7) S(1 – sin? 3t) cos 3t dt 8) ſ tan (5x) sec?(5x) dx cos? e

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Q: Suppose that f and h are integrable and that: frx) = -1 , , f(x) dx = 5 , ,h (x) dx = 4 ,Find: a. -2…

A: We have to find the given integrals.

Q: To evaluate sin42x cos 2x dx , the identities to be used is/are: sin22x = 1- cos?2x В cos²2x = 1-…

A: Check the identities

Q: sing reciprocal substitution *= the integral - dx reduces t I dz -1) 13 -dz (z?– 1) 1/3 zp- D dz

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Q: x2 dx Using trigonometric substitution, the integral is equivalent to V-4

A: Given∫24x2dxx2-4Substitute x = 2sinθDifferentiate x w.r.t θdx=2cosθdθNowIf x = 2…

Q: Af ter evaluation, if tan 43rdr=tan 3r- ( ?) tan3r +r + C, then find the missing (?) term. 9 A 3 B…

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Q: Evaluate each of the following indefinite integrals: Show complete and detailed solutions. Express…

A: Given problem :-

Q: Evakate: fcos 2xdx cos2x, cos 2x +C A sin2x sin 2x B 6 +C sin2x, sin 2x +C 6 2 cos2x cos 2x +C D 2

A: To evaluate: I=∫cos32x dx

Q: Question 16 n2x cos3x dx= sin5xdx - sinxdx A) True B False Question 17 csch2zdz=–In|csch2z –…

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Q: aluate each of the following indefinite integrals: Show complete and detailed solutions. Express…

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Q: Sa 4 tan e sec? Ode tan0-2tan 0–15

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Q: Given sec A = and that angle A is in Quadrant I, find the exact value of sin A in simplest radical…

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Q: Question 9 x² – 4 Evaluate: V A =Vx² - 4 – 2 sec-+ c =V x2 – 4 + sec¯ + C = 2/x? – 4 + sec + C D x2…

A: The integration of the integral is sqrt(x2-4)/x.

Q: If  ?⃗×?⃗ = ⟨−3,5,−4⟩ and ?⃗⋅?⃗ = 4, find tan(?), where ? is the angle between ?⃗ and ?⃗.

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Q: sin?u tan"u du where n is any integer, we use the transformation for tan?u = cos?u In A True B False

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Q: Which of the following will yield an inverse trigonometric function? S- wdw 25 – w2 dx В 9– 16x2 ydy…

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Q: Find the sum of the infinite geometric series 1 1 1 4 1 +.. 64 16

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Q: Question 20 ) dm: -2m cosh2m dm A) True B) False

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Q: ,In sin –1x ) dx / sin(e n sin -x -cos(sin-!x) +C V 1– x² | A True B False

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Q: In't dt 1. t(9-In?t)

A: The objective of the question is evaluate the indefinite integral.

Q: Which of the following is one of the correctIconvenient steps to evaluate| cot-4dx_which will yield…

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Q: Question 17 Which of the following is NOT an improper integral? x-dx A -2 Vx2-1 x/2 sec x dx 01 x13…

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Q: 4. Show that if x, y, z are integers such that x2 + y2 + z? = 2xyz, then x = y = z = 0. (H)

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Q: sin(e* ) dx sin - cos( sin-1x) + C 1-x

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Q: Find the critical points of the following function. 1 Inx f(x) =

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