Use Runge-Kutta's (4th order) method with a step size h=0.3 to intagrate the function y'=xy2-2xy from x=0 to h and y=0.619. (round off the answer to 4 decimal places)

Q: Reducible to Exact (2xy ln y)dx+(x2+y2√y2+1)dy=0 Have to be convert to exact by integration method

A: Given  Differntial equation (2xy ln y)dx+(x2+y2√y2+1)dy=0

Q: dx 3. J TxVx-1

A: the given integral is: ∫dxxx-1 we have to evaluate the given integral.

Q: dx = adt + bdz x = Xo + at

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Q: In Romberg integration, R42 is of order: 02

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

Q: Would you use numerical integration to evaluate. Explain.

A: We have given a definite integral;

Q: Integral in REVERSE ORDER

A: Given that  I=∫08∫y32ex4dx dy Limits are given y=0 and y=8     x=y3y=x3  and x=2

Q: Find the indefinite integral. (Use C for the constant of integration.) 4 zV 64z2 dz 49

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Q: (b) Use Romberg integration to compute dx 1+x correct to three decimal places.

A: Given: I=∫01 dx1+x  correct to 3 deecimal placesLet h=0.25,…

Q: 24/ Answer two from the following :- 2-x - Evaluate and change the order of integration in 1 = ²*xy…

A: We have to solve the given problem.

Q: Estimate Ay using differentials. .1/5 y = x5 e3x-1 a = 1, dx = 0.1 (Give your answer to four decimal…

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Q: Estimate Ay using differentials. y = x' 1/5 e3x-1, a = 1, dx = 0.1 (Give your answer to four decimal…

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Q: Evaluate with the order of integration reversed..... 4 11: x dx dy

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Q: Evaluate the integral. (Use C for the constant of integration.) 2 dx ex/2

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Q: Q3) Reverse the order of integration and evaluate the integral 8 2 dy dx y2 +1

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Q: Reverse the order of the integration dy dx sin x

A: W need to find integral.

Q: 2+x a) S dx x²+9

A: Given: I=∫2+xx2+9dx For evaluating given integral, first we separate terms then integrate it

Q: Q3) Reversing the order of integration 2 y² sinxy dy dx

A: Explanation of the solution is given below...

Q: dx 1. dt xt x(0) = 1, solve for x(0.3) when h = 0.1 I| -

A: Given function is, dxdt=-12xt,   x(0)=1, h=0.1 and we need to solve, x(0.3)   Here we have, (t0,…

Q: Integral from 1 to e of 5t^2 lnt dt

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Q: Find the antiderivative. (Use C for the constant of integration.) (8x + 9) dx

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Q: Q3] Use the trapezoidal rule of integration to determine the value of S, xlnx dx with h = 0.1, work…

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Q: Suppose the side length of a cube is measured to be 5 cm with an accuracy of 0.1 cm. a. Use…

A: The measurement of the side length is accurate to within 0.1 cm. Therefore,  -0.1≤dx≤0.1  The volume…

Q: Find the indefinite integral. (Use C for the constant of integration.) dz zV 49z2 - 9

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Q: 5. – 3t te dt

A: The given integral is: I=∫t e-3t dt

Q: To calculate x²e*dx dp, integration by parts is the best integration technique to use. O True O…

A: Explanation of the solution is given below...

Q: Find the differential dy of the given function. y = ln sqrt 5-x^2 dy=

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Q: 2: Change the order of integration. •ln 4 f(u, у)dydx.

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Q: Find the general indefinite integral. (Use C for the constant of integration.) ∫3v(v2+4)2dx

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Q: Find the indefinite integral. (Usec for the constant of integration.) (2ti + j 6k) dt

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Q: Evaluate with the order of integration reversed..... -√4-y x dx dy

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Q: Estimate Ay using differentials. y = x/5 e3x-1 a = 1, dx = 0.1 (Give your answer to four decimal…

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Q: dx y.= dy y arctan (-x 2a

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Q: Evaluate S(x + y)dxdy by reversing the order of integration.

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Q: Estimate the value of integral 3 to 1 dx/x

A: Given,  ∫131xdx

Q: Calculate the integration y+1 dydx

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Q: find the general selution of the differential equetion by the fimear methodi sxy'-2y=x

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Q: 24 Change the order of integration and evaluate dx dy. y²

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Q: First make a substitution and then use integration by parts to evaluate the integr 36 e dx

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Q: Find the antiderivative using the table of integration formulas. dx 2 324 - x

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Q: 3. Change the order of integration and evaluate L dydx ex log y 2

A: Please see the explanation below

Q: S S.(x + y)dxdy by reversing the order of integration.

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Q: Suppose the side length of a cube is measured to be 5cm with an accuracy of 0.1cm. a) use…

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Q: Evaluate S.(x + y)dxdy by reversing the order of integration.

A: answer is in next step

Q: Find the total differential. z = 10x y10 dz =

A: As we know that the: If the given function is z=fx,y then the expression for the total differential…

Q: y() 2. Determine the constant of integration for the following: - dy 3cosx 6 given y dx

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Q: 3. Estimate the value of the integral 1 dx (n = 4) using Trapezoidal rule. 1+ln x

A: The value of h in the trapezoidal rule is h = b-anh = 5-34h = 24h = 0.5 Form a table with the x…

Q: S e2x x2 dx

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Q: 24) Find the integration by applying (by part method) Sin ¹y dy

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