Integrate by parts: ex sin x dx 2.

Q: The value of | sin(x + y) dx dy is

A: We will use the fact that  sin(x+y)=sinx cosy +cosx siny to evaluate the given integral.

Q: m. n. Sex: [ tan³ x dx ex sec³ ex dx

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Q: |(xsin(3x)) dx XS

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Q: Differentiate (a). y = 23z+sin z² %3D (b). y = r³3=

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Q: y = sin(x) at |0, 0, with four equally – spaced points

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Q: Find dy/dr. cos 2r y = sec r+ 1

A: solution :-To find :- dydxy=cos2xsecx+15=ddxf(x)g(x)=g(x).f'(x)-f(x)g;(x)[g(x)]2

Q: The integration of ſ, Vx tan-'Vx dx is

A: Given that  The integral is

Q: dy y3 , У (0) : 1 dx 1– 2xy2

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Q: Integrate by Substitution. 1. dx where u = Vx+2 2Vx+2

A: By using substitution method, we calculate the given integral.

Q: To evaluate fx (cos x2)e* dx, use integration by parts. What is the best choice for u and du?

A: Consider the provided integral, ∫ xcosx2ex2dx Evaluate the provided integral. Apply the substitution…

Q: Evaluate using Integration by Parts. -8x sin x dx + C

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Q: use the methad of variati on of param eters to solve the equation d?y %3D dx? |+ Cos 2x

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Q: dxdy Vy X'

A: Given: ∫01∫yy21y2-x2dxdy

Q: Given x = 2 cost + 38 and y = 5 sin2t %3D

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Q: Q3 Integrate using trigonometric substitution: dx I To +x² /9 +

A: Let (x/3) = tant Differentiate on both side  dx/3 = sec2t.dt dx = 3.sec2t.dt

Q: d) y = sin*(x'/3) + arctan(r?)

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Q: (b) Calculate fe" con(r2) dz using integration by parts as many times as necessary.

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Q: п sin ydx + cos²xdy = 0; y (÷) =| %3D 4

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Q: se C for the constant oT integration.) (7 cos x + 3 sin x) dx

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Q: y Sin (x) dx dy -2 2.

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Q: d'y = 4 sec 2x tan 2x, y' (0) = 4, y (0) = -1 dx?

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Q: 2 dy Is y = sin t, a solution to = 1 – y? Justify-

A: We will prove the given statement.

Q: integrate by parts t7 sin⁡(2t4 )dt

A: We have given indefinite integration with respect to x. While solving the indefinite integral, we…

Q: rcosA 2. r sin 0 dz dr de

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Q: dy Solve the DE. x +x = sin (x + y) dx

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Q: if y^3 + y = 2 cos x, find the value of d2y/dx2 at the point (0, 1).

A: Given,

Q: Solve the DE using Variation of Parameters: y"+y = sec' x %3D

A: Given  The differential equation using variation of parameters. y''+y=sec3x

Q: d'y +2 sin y cos' y = 0. dx 6. If y= tanx, show that

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Q: .2 x cos?y dx + tan y dy = 0

A: The given differential equation is  x cos2y dx+tan y dy=0 Solving the the given differential…

Q: cos(x + y), when x = 0,y = dx 2 = dy : %3D

A: To solve the differential equation we can use a substitution u=x+y and then we can use variable…

Q: J sin“ x dx е.

A: Let,    I = ∫sin6xdx  .....(1)  = ∫sin5x.sin x dx    Now we solve this integration by using rule of…

Q: Given a = 2 cost+35 and y =7sin t %3D dx dt dy dt |3|

A: Topic : differentiation

Q: If r = (cost)i + (sin t)j + 2tk, find r × dr/dt.

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Q: dy Find xp. y = tan -1( In 2x°) %3D dy xp

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Q: * = cos(x + y), when x = 0,y = = %3D dx

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Q: Find dy/dx

A: To find the derivative of y=∫x0sint2dt. We know that, ddx∫xafxdx=-fx Therefore,…

Q: (у3 — у?sinx — х)dx + (3хy2 + 2усosx)dy %3D 0

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Q: Using the substitution x = sec 0, dx S: J x2Vx2 _ 1 where x > 1, is equal to

A: We can find the answer as below.

Q: Find the intergral of i. SVīdx ii. (x - 1)dx

A: According to Bartley guidelines I have, to solve only first question so repost the problem for…

Q: evaluate using Integration by Parts, substitution, or both if necessary.

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Q: - y = V1 – sinx

A: Given,y=1-sinx3y=1-sin(x)13Differentiate w.r.t. x using chain…

Q: sinx dx 5+ cor?x

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Q: | sec? (y) /2+ tan(y) dy V

A: To evaluate: ∫0π sec2y 2+tan ydy

Q: dt J (cost)?V1+ tant COS

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Q: 3 3 У(х'у + 2х — у)dx + x (ху — 2) dy 3D 0 3

A: Firstly we find Integrating factor, then find general solution.

Q: Find F dX, where x= 3 cost y= 1+3 sin 2r)

A: Given It has to find line integral of given parametrically curves Where

Q: Solve the fo llowing D.- E y + y tan X Cos X %3D

A: