Determine the avarage Valve of + he Aunction fex)=Cas(z)-Sin Cx/2) PA L-2, by using The meen vaelve Theoren fot integros

Q: Evaluate the integral. er HEAD ² y³ In(x) dx, y> 0 ind

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Q: In ir le) secx dx to be integrable using the formula What should be the value of A for 2- sec x…

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Q: Show that [ xdhy – ydy c Vx*+y² is independent of any path of integration which does not pass…

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Q: 1- Use trapezium's Rule with n = 4 to approximate the integral Vx dx

A: We have to use formula of Trapezoid Rule.

Q: Evaluate the iterated integral: dydx. /4 Jx²

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Q: Q0 Integrate 2 from x? o to L x²_2 trapezaidal rule with four

A: SolutionIntegrate x2-2 from 0 to 4using the trapezoidal rule with 4 bandsFormula of trapezoidal…

Q: Evaluate the integral (2x +3y)dx + (27x – y)dy along the parabolic arc y = x² from (0,0) to (1, 1).…

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Q: Evaluate the double integral sin(y' +1)dydx.

A: Use the change of order of integration to solve this problem.

Q: 2. Given that f(t) = f cos x cos(t − x) dx, fin integral.

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Q: Show that ∫0∞ e-x 2 dx = ∫10√(-ln y)  dy  by interpreting theintegrals as areas.

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Q: 7. Change the order of integrations to find iterated integral (dydx. 2

A: Given that, integral, According to the limits of integration of the given integral, the region of…

Q: find the derivativa dy for the frurrtion y=x by using lagarithmic differatiation.

A: Given y=x5x Taking logarithmic both sides, lny=lnx5x implies lny=5xlnx

Q: b) Estimate the integral esindx using composite traperoidal rule with h= 0.25.

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Q: Сompute 1. f dx, where f(x)=|x|.

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Q: Evaluate the double integral : dy dz

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Q: 3/ Find Valke of integral Sx dx

A: Value of the integration

Q: Ue fe Einemial Theorem to ine tre coeficit ofnthe eparsion of ir+ 31

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Q: Сompute L f dx, where f(x)=|x|.

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Q: Exampley Consider the following nonlinear sine-Gordon equation Utt-Uxx+5 inu zo subject to the…

A: Solution: Given the Sine-Gordon equation utt-uxx+sinu=0   - - - - - (1) and initially conditions;…

Q: dv Integrate ду 1 partially with respect to y. II

A: To partially integrate the given function with respect to y, implies x will be treated as a constant

Q: By exchanging the order of the integration, the evaluation of siny dydx y klea

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Q: A// compute $(4+ e*) dx+ (siny + 3x*)dy Where c is closed bounded region lying in the first quarter…

A: See the attachment

Q: 4.) evalnate the integral dx aresinx a. WI-Y b) S x arctanx dx

A: We have to solve

Q: What is the integrable form of et dx? e-e-X

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Q: In evaluating, 2x cos (2x) dx using integration by parts, identify the portion of the integrand to…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Evaluate the integral / (10x + 15y)dx + (18x – y)dy along the paraboli - arc y = x² from (0,0) to…

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Q: Compute for the value of constant (C) by solving the given DE using integrable combination. Let x=1,…

A: Given xdy-ydx=4x4dx

Q: Find the path y = y(x) for which the integral 1. r2 VaVi+y(xdx is stationary.

A: The path y = y(x) for which the integral is stationary satisfies Euler’s equation given by,

Q: Find the approximation of the integral. 1= [e*dx Using Romberg's rule derived from Trapezoidal rule…

A: Given integral I=∫01e-x2dx Here we use Romberg's rule derived from Trapezoidal rule for 1,2,4,8…

Q: Evaluate the integral (12x + 15y)dx + (24x – y)dy along the paraboli arc y = x from (0,0) to (1,1).…

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Q: 2) Show that the integral f. (cosyz dx – xz sinyz dy - xy sinyz dz) is path independent and find its…

A: Condition for line integral to be path independent is given below. ∫cFdr is path independent if F…

Q: Find the integration of S ecosx dx using Trapezoidal and Simpson's Rules

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Q: Evaluate the iterated double integral: esec y+1 dy dx. VE sin y sec

A: To evaluate the iterated double integral :               ∫14∫sec-1xπ3  esecy+1sin ydydx

Q: Evaluate the integral / (2x + 12y)dx + (24x – y)dy along the parabo arc y = x² from (0,0) to (1, 1).…

A: Solution is below

Q: is the follecing dif Mantial opuatíon Jmeo on mot Y with x>1. ey-x

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Q: Evaluate the integral (8 (8x+15y)dx + (27x - y)dy along the parabolic arc y = x² from (0,0) to…

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Q: Evaluate the line integral. -y dx + x dy segment from (3, 0) to (0, 3) x2 + y2

A: Find the slope of the line through the given points.

Q: 1. Estimate the integral using Trapezoidal approximation rule with n=4: 2 + t)dt

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Q: Evaluate the integral (8x +9y)dx + (3x − y)dy along the parabolic arc y = x² from (0,0) to (1,1).…

A: We can observe that x is ranging from 0 to 1. We have the following. So,…

Q: Find the limits of integration in cylindrical

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Q: (i) Change the order of integration in the integral. Wi-x dx dy and hence evaluate.

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

Q: Evaluate the in tegral (x+ 2y) dy

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Q: Compute for the value of constant (C) by solving the given DE using integrable combination. Let x=1,…

A: Use by exact form

Q: Show that {zn}nEN is Cauchy, where z, = sint dt. 1+t

A: Sol

Q: (5) Obtain the integral curve for dy +y cotx = e*cscx passing through the dx point (0, 0).

A: We have to solve the given differential equation

Q: Evaluate the integral / (12x + 18y)dx + (12x – y)dy along the paraboli - arc y = x² from (0,0) to…

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Q: FCx) is continoos on L3,5) and S Fex) dx= 5 Evaluate integral

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Q: ⌠13(e0.5x+sin2x)dx, use n=4

A: We will answer the first question as you didn't mention any. Please resubmit the other question…

Q: Calculate I dx n=LobysimPsons4) rule

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Q: dydx tan x 1. 1+ y²

A: We need to calculate double integral in given order dydx   we use result of inverse Trigonometry…

Numerical Integration

In a mathematical investigation, numerical integration comprises a wide group of calculations for computing the mathematical estimation of definite integral, and likewise, the term is moreover in some cases used to depict the numerical solution of differential equations. The most important aspect of this theory is error analysis.