Compute y = S V1 -x dx using Monte Carlo Method. The integral is approximately 1.5708

Q: Evaluate the double integral S S (11a°y³ + 11eš")dædy

A: We have to evaluate ∫36∫2611x3y8+11e5x dxdy   We evaluate this double integral using iterated…

Q: Solve the solution of the DE of the Gompertz function: dP = c In[P dt М In[P

A: We have a nonlinear ordinary differential equation :

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

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Q: The particular Integral for (D² + 19²)y = sin19z is Yp 38 O Yp 19 O None O Yp Zacon19z 38

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Q: 3. S "(o2-1)dv v2+1

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Q: in S 0 n soo

A: Here we have to Evaluate the double integral

Q: e3t dt 2 (1+4e*)

A: Please refer the attached image for complete solution.

Q: Evaluate the integrals in ∫2ey cos ey dv

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Q: 1 (b) Evaluate the integral S ; dx 2x2-12x+26

A: To evaluate: The integral of . Formula used: Integration Formula:

Q: s(s - 1)° ds

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Q: Evaluate the integral. 4π S t² sin(2t) dt

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Q: Evaluate the Integrals S(** - 8x + 7)dx а. 3 dt b. Jo 1-16

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Q: dx 1 = [- 1+vx+1

A: To evaluate: I=∫dx1+x+1

Q: Evaluate the integrals

A: Given: ∫-3-1y5-2yy3dy for evaluating this limit we first separate terms then integrate it

Q: Approximate the integral using Taylor series method 1 f(x) = sin?x dx %3D x2 -1

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Q: 2. a) Evalute the following improper integrals 6. dx 3 3

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 2. Compute the integral dy dx by interchanging the order of integration.

A: Order of change of integrals

Q: The particular Integral of D'y = = -5 is O yp = 00 O Yp = 0 O Yp = -5z O None of the choices Yp =

A: Given that,

Q: Evaluate the double integral S' Sí a³y²dxdy..

A: Given that double integration and we solve it by using general property of integration. Here i…

Q: Evaluate the integral.

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Q: 1) Find the following integrals: a) S dx 3x+1

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: The particular Integral of Dy = -5 is Yp = 00 Yp = 0 Yp = -5x O None of the choices Yp 2

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Q: (a) Evalate the integral||xydy dx. 12

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Q: The improper integral J dx converges to x-5 4 о попе 1

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

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Q: The particular integral of (D² +1)y = x is

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Q: 2 Evaluate the improper integral e2a dx, if exists.

A: Evaluate the improper integral  ∫-∞2 e2x dx

Q: show the steps of this integral: | dxp In p = In a H

A: Given that H=-∫0adxρlnρ This can be written as, H=∫0a1ρdρ

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

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Q: 3. Show that for p> 1 and r E (0, 1), the integral below converge: dt tp

A: by limit convergence test we cab prove this, we have to treat the definite integral as summation…

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: 5x dx. - 6 Compute the integral x2

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Q: 1 . Evaluate the integral: S, S (4x³ + 6xy - 3y²) dx dy -1

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Q: Compute the integral 4x /5 – e2¤ dx. e

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Q: In Evaluate the integral: Sé e x²+3x-7 x-2 dx

A: Option (b) x22+5x+3ln|x-2|+C

Q: Evaluate the integral -6y dy e2y

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Q: Find the net change in ve]locity over [1, 4] of an object with a(t) = 8t − t2 m/s2.

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Q: 3. Estimate the integral v2 + x² dx using appropriate of Simpson's rule with step size, h = 0.2.

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Q: Evaluate the integral: S dx (x+6)(x-4) ← +C

A: Given problem:-

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 any value of c for which the improper integral cx + 36 x2 + 1 9. da x (4 x + 5) converges.

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Q: S √x²-a² X dx

A: To solve the given integral.

Q: 2. a) Evalute the following improper integrals dx Vx – 3

A: We will solve the problem.

Q: Find the integral. 21) + e3t) dt

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Q: The particular integral of y" + 5y' + 4y = 3x +2 is

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Q: dx Evaluate the given integral: S- xV5x2-4

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