4[8,(t-2) rect(r)dt

Q: Evaluate the integral. 8e 8t dt 8t 2. 1+ e 8t 8 e dt = 8t 1+e

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Q: 7.S dt J VE+2- 5

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Q: Find the total differential. z = 9x4y9

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Q: |(7) In general, SUT S (SUT)', but (SU T)' S°UT. Pra

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Q: 2. given that y = 0 at r=1

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Q: & b. su j+ byz²

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Q: Show that Ě = 3xyê+G)+2Ê is R3 and Pind Conservative a potential Ø Rar F. on

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Q: 2x For x > 0, In (t +1) dt %3D da A In (2 +1) In (8z + 1) 2 In (2 + 1) 3. 2 In (8z +1) E 24x In (8z…

A: Considering the derivative of the integral

Q: What is the general solution of the following ODE y' - (2y/x) = 3x3 Hint: Use integration factor…

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Q: Find the total differential z = 2x3y − 8xy4

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Q: 1. Evaluate the ff. integral f, (5x6 + 3x³ + 6)dx ·1

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Q: Express the general solution of dy/dx = 1+ 2xy in terms of the error function erf(4) = dt.

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Q: p = m(1-dt) for d (buisness)

A: In this question , we can solve for 'd'.

Q: Integral of (dt)/(t^2sqrt(t^2-16))

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Q: What is G = xy ax – x²y ay + 2y az at B(3, –4, 1), expressed in SCS?

A: Given: G→=xy ax-x2y ay+2y az -----------(1) Where, Bx,y,z=B3,-4,1 --------(2)

Q: Step by step

A: Given integral

Q: Evaluate the integral fe (2x+4) (x² + 4x + 2) dx n- by making the substitution u = x²+ 4x +2.

A: In the question we have to find the integral of the given function.

Q: Evaluate the integral dx (7x + 6)2 by making the appropriate substitution: u = dx (7x + 6)

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Q: 4. Find the Cauchy principal values of the following integral: dx. (x²+1)(x²+2x+2)

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Q: 13. - (In t ² )º t dt

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Q: 3 c3 4. Evaluate the integral S ex+ydydx '2

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Q: Evaluate the integral : S 8x2+10x-6 (x-1)(x+1)z dx (2—1)(ӕ+1)? +C

A: Given: ∫8x2+10x-6x-1x+12dx To do: Evaluate the given integral.

Q: Evaluate the integral. 8t 8 e S dt 1+ e 8t 8e 1+e 8t 8t dt =

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Q: 2. Integrate: S w5 V7+ w3 dw 3. Find S (6-+ - sV) de

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Q: If 3 h(t)dt = 5 5 and .3 h(t)dt = 7.3 what does the following integral equal? h(t)dt =

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Q: ar integral of the c 3 – 7D2 + 7D – 2

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Q: Integrate the following: ,S (x4 – 5æ³ + 6) dæ - 1. So(1- r)*dz su(1– 2.

A: These questions are related to indefinite integration, we will use use integration formulas and…

Q: 2): Consider the DE y" – y" – 6y = 0 -

A: Follow the procedure given below.

Q: (z In z + 5)dz

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Q: 10. Using the substitution u 2x - 1, prove that %3D 3 8 dx J1 (2x-1) 25

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Q: a) dt 9 =dx xVln x b)

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Q: (x) = 3x +12x+2, %3D ues of a, b and c such that

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Q: J sec° (10t) tan“ (10r) dt 4 10.

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Q: 3 In (sec v) 2t Evaluate the integral ex dx dt dv. 00

A: Topic = Integration

Q: So So t² etu du dt

A: Given, ∫03∫0tt2etududt

Q: Compute sec? z + x) dr

A: Given : ∫12sec2x + xdx

Q: Evaluate the integral. 2 2 t+ dt 15 OA. 29 О В. 6

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Q: d tanh¬' (In t) = dt 1(1 – (In t)²)

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Q: Find the antiderivative of: dt/(1-7t)^3 where  u = 1-7t

A: To find antiderivative

Q: Compute the fUlNOW 1 dt t2 + 1 d. dx 1

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Q: 2. Evaluate the integral, 6(t-1)8(t-2)dt j8(4-1)6(1-2)dt

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Q: 4 In(t) dt

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Q: evaluate the Cauchy principal value of the given improper integral. roo 1 dx 6x + 25 | roo x2 dx (x2…

A: The Cauchy principal values of the given improper integrals areevaluated as shown below.

Q: What value of x > -1 maximizes the integral / t²(3 – t)dt?

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Q: 3t e"dt 2 (1+4e3

A: Let's integrate.

Q: Find dr. J (1+z²)3/2 - In Vx² + 1 + x| + In |Vx² + 1 + x| - Ja? + 1 +c Vx² + 1 O Option 3 Option 1…

A: Let I= ∫x21+x232dx Let x=tanθ ⇒dx = sec2θdθ Substituting this in I, we get

Q: Use the substitution formula to evaluate the integral. 2/5 dt v/252 -1 -2/5

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Q: Q2: Evaluate the integral S Vx² – 2x + 1 · dx 3,

A: To Evaluate: