we Show that far Re (2) >1 c= r(2) J(2)

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

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Q: Find the value of ds / du at u = 2 if s = t2 + 5t andt = (u2 + 2u)1/3.

A: We first find ds/dt and dt/du

Q: 2) Refer to sections 1,2,3 in the course notes. Compute the integral: S (3e' – 4 )dt

A:

Q: is given by Oxy = E(XY) HxHy.

A:

Q: 14. Evaluate the integral. 4 (y - 2)(2y + 1) dy

A: Given that : The integral is ∫04 ( y - 2) ( 2y +1) dy

Q: Evaluate S dz over C, where C: |2+1| =1 O i pi

A:

Q: d If g(x)=- -S*[e' - In (21+1)]dt, find g(x) Se dx 4 A (2x+1)² 4 B e+ (2x + 1)² Ⓒe* -In (2x+1) 2 D…

A:

Q: In VVi+1-2 dt, if we let V Vt+1 – 2, then dt is equal to A 2(x²+2)dx ® 4x(x²+2)dx c) None D…

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Q: - If W = xy + y2+1 azw Show that a2w ey %3D дхду дудх

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Q: In t+1-2 dt, if we let V Vt+1-2, then dt is equal to A (4x³ + 2) dx B) None 2(x²+2)dx D 4x³dx 4x…

A:

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

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Q: QUESTION 1. EVALUATE. J 1 dx V9x2+4 In (/9z² +4+3zl) +C 3 ||

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Q: 2 Evaluate the integral S (3x³ – 2x² + x) dx. 1

A: We solve it by integrating polynomial

Q: The definite integral (10+-2-3-ar+5)dx is equivalent to A 2 (at- 3r+ 5)de B 2(10-2-6r) ds…

A: LetI=∫-5510x5+x4-2x3-3x2-6x+5dxWe know that ∫-aax2n+1dx=0Apply the Sum Rule:…

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

A:

Q: In +1- 2 dt, if we let V Vt+1-2, then dt is equal to t+1– 2, then dt is equal to A) None 4x³dx ©…

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Q: In t+1-2 dt, if we let t+1-2, then dt is equal to A 2(x2+2)dx (в 4x³dx O 4x(x2+2)dx D None E…

A: Option C is correct.

Q: 3.Evaluate ex dx, by Simpson's ½ rule. n=6` 1 = (b − a) ƒ (xo) + 4f (x₂) + 6 f(x₂)

A: We have to solve by Composite Trapezoidal Method.

Q: Evaluate the integral.

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Q: 1 So 2t en + e-2t ezt - e-at dt

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Q: S dy 7 y2-8y+5

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Q: Suppose that a) [15x²y; 0<x<y<1 f(x, y) = { 0; otherwise. Compute E(Xy), Var(X) and Var(Y). b)…

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Q: the integral S(x³ – 2x – 1)e-*+1dx is equal to:

A:

Q: .2 3. If o (x) = f Ví dt, then 0 (a) 2x2 (c) O do dx (6) SA (d) 1. is

A: ϕx=∫0x2tdt

Q: de xdx 1. (In* 4x-1) 2. V3x +5 sin 4x de de 4. 9+8cos 2x 3. (5x-3)dr 5. 3x-3x+2 (3-4x)dx 6. TAx…

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Q: •1 cln(5) 1- S SmS) xy evx ´dydx r

A:

Q: Question 1 Prove that 4 = ucy)e is a Solution for d24 - y°4 = 0 dy?

A: Given differential equation is d2ψdy2-y2ψ=0         (1) We have to check ψ=u(y)e-y22 is the solution…

Q: To prove that 2 dx 2 In V1 + (In x)² + In x| + C X/1+ (In x)² we use the substitutions

A: The given integral is ∫2 dxx1+lnx2 Find your answer below

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: If g(x) = - - S^*[e'- In(2t+1)]dt, find g'(x) . dx A ex-In(2x+1) 4 B

A: We can solve this as follows:

Q: S 1.Prove that L (coswt) = %3D s2+w2

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Q: 20 Given that the (bx) +(ay) =(ab), where a and b are constants. Show that-

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Q: 2 If [ In(ax)dx = 2, then a %3D 1 e4 4 None es 4 4 4

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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: By the Fundamental Theorem of Calculus: •t „2 +1 dx 5x +1 d dt d and dt - 6t x2 +1 dx 5x +1 d…

A: Given

Q: EX~U(0,1) if Y= =L l(t-x)~ Exporential (A,

A: From the given information, X~U0,1 The probability density function for X is, f(x)=11-0       =1,…

Q: If you are trying to solve f et dx and you let u = e then: dv = du = v = vdu Write down the uv –…

A:

Q: In(|(2 +1)"(z + 3)|l) 15x - 13 dx = X (Don't forget to include the constant of 2-2x 3…

A: topic - indefinite integral

Q: Show that S ťe dt = 3VI

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Q: If s = 3/t + 1, then ds Preview %3D dt

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Q: %3D in Fin d E(S an d Var(s)

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Q: 2 1 Evaluate the iterated integral S 18*y°dy dx. -2 0

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Q: 3. Express the general solution in terms of Bessel functions: z²y" + 4ry' + (x² + 2)y = 0

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: 3+ Evaluate the integral: e³+ cosh2x33+ cosh2xsinh2x dx (3e)3+ sinh2x A +C 2+In3 (3e)3 + cosh2x +C…

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Q: 23: Evaluate the integral of ſ (5y+7) 5 dy

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Q: L{sin(JF)} = V %3D 4s 2.s2

A:

Q: 5. What is the most general antiderivative of the function S(2) = z - 2, in other words, what is -…

A:

Q: ds if s = dt t Find 7t +2

A: S=t7t+2 We need to find dSdt