II. Find the following indefinite integral. 4 -5y + ye +r sec" y - 7) dy 1. + 2? - z+1 dz 2. 1+22

Q: me result of the integral in 0 given | V ²– 25 -dy is 5 tane – 50 +C , y A) True B) False

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Q: Which of the following integrals represents the length of the curve y = 2*, 0 < x < 3? 3 VI+ 2* dx…

A: Given function :

Q: 14 Find the integrals using integration by parts. a. fx(x + 4)°dx c. fr'e"dr

A: As per our guidelines I am solving only first three parts of the question please resubmit the other…

Q: I. Evaluate the following integrals. 1. Sx sin 3x? dx tan y 2. S dy 1-tan²y 3. S sec?(3 – 2t)dt

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Q: Evaluate the iterated integral. 17 [₁₁/₁² (x² + y²) dx dy = i 17 LL" (2² + y²) dx dy

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Q: Use the Table of Integrals to evaluate the integral. (Use C for the constant of integration.) yV 6 +…

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Q: V2y? – 3 dy y?

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Q: Evaluate the iterated integral. ITT*³. /0 10 6ze-x6 dy dx dz

A: Integrate usually but first with respect to y then x then z.

Q: Evaluate the iterated integral. 3 I (* + 5)dy dx 3 8 (x + 5)dy dx = i

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Q: y + 2 "hat is the indefinite integral of JC² - 1)(² + 1 )" dy ? 2 (y² – 1) (x² + 1

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Q: y5 dy; 4 + y*

A: The given integral is ∫y54+y4dy  ...... (1) Substitute u=y2 . This implies  y=u Differentiate u=y2…

Q: Which of the following definite integrals gives the length of the arc y - 1 + 16x-dy 0 16y – 15 이 0…

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Q: 3. Calculate the following integrals: (a) So 43 dx. (b) S x5-° dr. 1 (c) J 1Te- dr.

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Q: Evaluate the integral. integral y e 2y dy

A: Evaluate ∫ye2ydy

Q: Evaluate the indefinite integral. 15y dy J(y – 4)(y² + 4)

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Q: Find the indefinite integral. (Use C for the constant of integratic 8 dz zV 4z2 - 25 V 4r – 25 -tan…

A: Given query is to find integration of the expression.

Q: Evaluate the iterated integral. 9. 2ye-X dy dx

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Q: Determine the following indefinite integral. 1 dy 14y

A: To evaluate:   ∫114ydy Property of integration used, 1. ∫cfxdx=c∫fxdx                           …12.…

Q: 4. Calculate the following iterated integrals by hand. Show all steps. (a) (b) (c) -dr dy

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Q: Evaluate the definite integral. 2exin ( z ) cos(z)dz 0.

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Q: Evaluate the iterated integral. 27 1²th I 729- y dx dy = 27 1.² 1. 729-y² y dx dy

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Q: b) Evaluate the integral E (1+ etane) Sec20 de

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Q: Find the following indefinite integral. |(4cos(y) – 2sec(y)tan(y))dy

A: Explanation of the answer is as follows

Q: Evaluate the iterated integral. 4 5 6 (x² + y² + z²) dx dy dz -4 0 0 5 6 (x + y? + 2? )dx dy dz = i…

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Q: 2. Evaluate the indefinite integrals: D = tan r secʻ r dr 8x + 7 dr 72 +1 E = - 2dr F = dr V9 - 36x2

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Q: Sketch and evaluate the reverse integral 3. dy dz

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Q: Evaluate the I'S. ü integral 2x-X xy dy dx

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Q: Which of the following integrals is equal to the integral / f(3x – 5) dx? 713 f(2) dz 7/3 f(2) dz -2…

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Q: Evaluate the iterated integral. 16 3 x²y dx dy 16 3 Py dx dy : i

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Q: aluate the integral / (8 x + 18y)dx + (24x – y)dy alor y = x² from (0, 0) to (1, 1). TE: Enter the…

A: Topic:- application of integration

Q: 12. Determine the following integrals. Do not simplify. (a) / (5z* + V#) dz (b) dr dy = r1. dr 13.…

A: ∫5x3+x53.dx=∫5x3.dx+∫x53.dx=5.x3+13+1+x53+153+1+K,  (where K is an arbitrary constant)=5x44+38x83+K…

Q: 25. Describe the domain of integration of the following integral: LLE /5-x2=22 f(x, y, z) dy dx dz…

A: Domain can be discovered using the bounds of the integral. Domain is 1≤y≤5-x2-z2.

Q: Find the general indefinite integral using definition. (3t*-t3+6t2 b) S(3 sin x – 4e* + 5* + 6) dx -

A: Integration Question

Q: Which one of the following double integrals is equivalent to the integral 2x-x2 Vx2 + y2 dy dx? 0.…

A: The integral in Cartesian coordinates is : We first try to look at the region of integration here:…

Q: 4) Evaluate the following indefinite integrals. a. S (+ V3 - dx 4 3x2 b. S (2 sec2 x- 5 cscx cot…

A: Integrare

Q: Q2. Evaluate the iterated integral by changing the order to dx dy. eu dy dx

A: For reversing the integration order, we will replace the limit of x and y with interchangeably. Then…

Q: x dx S- V1+x²V1+x? =? 2 2

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Q: Which of the following integrals is equal to the integral / f(3x – 5) dx? 7/3 zP (?)f s(2) dz 2. 7/3…

A: Topic = Integration

Q: Which of the following integrals is equal to the integral / s(3x-5) dr? A f(2) dz 7/3 B | s(2) dz 2…

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Q: 1 dy dx as an iterated integral. x°y Evaluate the improper integral

A: ∫8∞∫e-x11x3ydy dx=∫8∞1x3[ln y]e-x1dx = ∫8∞1x3[ln1 - lne-x]dx{ ln1 = 0 }, {ln e-x= -x.1}= ∫8∞1x3[0 -…

Q: Evaluate the line integral 11y dy over y = x for 0 < x < 3. (Use symbolic notation and fractions…

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Q: Evaluate the iterated integral. 5 (бх — 10y) dy dx -1 5 (бх — 10у) dy dx%3 i

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Q: 14. VE (t² + 3t + 2) dt

A: We use the formula integration of xn dx=xn+1/(n+1). See 2nd step.

Q: 7/2 VI- cos z dy dx dz

A: The detailed solution is as follows:

Q: Q3. Evaluate the following Integrals Stan* 0 sece de I. 2-16 хр- Vx II.

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