Show: 2 x + 2 sin dydx + 2y 1 va sin-dydx = 4 2y 2 va

Q: y'sin = y cos a is solvable by?

A: given equation y' sinπx = y cosπx is solvable by separation of variables

Q: 2-) Calcu late +he folloming integ rols by using the integration met hods a)| (hx" +8x²+ 15x) dx dx…

A: We are allow to solve one que at a time

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

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

Q: Solve using Substitution Method. y(x Tan x + In y)dx + Tan x dy 0

A: The substitution method as follows, y (x tanx + ln y) dx + tanx dy = 0

Q: To evaluate the integral |(2x+1)tan Vx dx using Integration by Parts, we should choose

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Q: dy 3. 1+ sin 4y

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Q: Differentiate: y = 5 tan? (25z) %3D Oy = -750z tan (25z) sec (25r') Oy = -750z? tan (25z) sec (25z)…

A: We have to differentiate  y = 5 tan225x3.

Q: Determine the constants a and b such that                                                       sin…

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Q: Find the area.   y = 3 cos(4x),    y = 3 − 3 cos(4x),    0 ≤ x ≤ π/4

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Q: Calculate the integral (а) dx (*/3 Vtan 0 (b) п/4 -do sin 20

A: Given : (a)  ∫-∞∞x5e-x2 dx    (b) ∫π4π3tanθsin2θdθ

Q: sin 2ydy 4 – 3 cos 2y

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Q: Use integration by parts to evaluate 2x cos (x) dx

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Q: 2. [2x*tan y – ysin (2) – 1] dx + [xsin (2) + x*sec*y] dy =

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Q: (ysin x+xy cos x)dx+(xsin x+1)dy = 0 Ans. xy sin x+ y = c

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Q: Differentiate y = In ( sin² (4x)). A y' = 8 tan (4x) y' = 8 cot (4x) y' = 8 csc2 (4x) sin (8x) y' =…

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Q: Find dy/dx 1. sin^−1(xy) = cos^−1(x − y) 2. sec^−1(2y cos x) = x^y

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Q: 2. Find if y = esinvx dx A. (sin vx)esin vã-1 cos vx В. (esin væ) 2 vx e Cos vã С. 2 vx (cos Vx)esin…

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Q: plot parucul Solu 1. y" +3y' – 4y= sin wx, 2. y" +3y' – 4y = cos wx.

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Q: Show that: 2 2 4: +2} | sin 2y x=1 y=vx TOX dydx = 2y dydx+ _3 x=2_y=vX

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Q: followin COSX 3. f- dx 1+sinx 4. f (sinx + cos x)² dx 203 (y² +1) 20 dy 5. f

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Q: sin(6y) sin(8y) dy.

A: Topic - integration

Q: ACTÍVITY 2: Differentiate the 1) y = -2 sin 2) s (t) = - WE

A: Apply the differentiation rules for the trigonometric functions to get the derivatives of the given…

Q: Solve (1+siny)dylx=[(2ycosy-(secy+tany)]dy.

A: This question is taken from a differential equation in which we have to solve the equation and take…

Q: (x' cos(x')dx = %3D

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Q: y'' + 3y' + 2y = sin ex

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Q: 2T sin (2) dydx 0,

A: To evaluate the double integral, ∫π2π∫0x3sinyxdydx.…

Q: Differentiate: y = ln cosh (cos 2x) 3. O y = 6 sin 2x tanh(cos 2x) %3D O y = 6 sin 2x coth(cos 2x)…

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Q: Find the area of a triangle bounded by lines y=2x and x=1 by double integration

A: Given region, y=2x        ...(1)x = 1        ...(2) Substitute the value of x = 1 in (1), y = 2 So…

Q: S sin x In(1 + sin x) dx

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Q: The integrating factor of the linear first order differ dy sin2x y+tanx xp Oa None of these Ob sinx…

A: Given differential equation, sin2xdydx=y+tanxdydx-ysin2x=12cos2x If the equation is of the form…

Q: vE zy sin{z° + y)dzdy Find

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Q: sin y cos(cos y)dy

A: We have to evaluate the integral: ∫sin y coscos ydy In this case we will use substitution method. So…

Q: Find where w= cos z - cos x cos 2y + sin x sin 2y and z x+2y. Me.

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Q: Evaluate: S 0 tan¬(0)d0 arctan(8)–0 Sarctan 0 + C 2 arctan(0) 0 zarctan 0 + C 2 arctan 0- 0…

A: Please refer the attached image for complete solution.

Q: The value that will satisfy potentia. function p is x + y sin x None = In (x +y %3D

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

Q: Evaluate by Integration by parts (IBP): 4. x° cos 2x dx

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Q: Find dy dx if sin(x + y) = tan(xy)

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Q: Integrate by parts: ex sin x dx 2.

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Q: Apply integration by parts: S udv - S vdu = uV sin2x – cos2x dx sin2x + cos2x

A: Given function is sin 2x-cos 2xsin 2x+cos 2x. Integrate using integration by parts. Chain rule of…

Q: Integrate by parts f(x)=sin4(x)cos3 (x) dx

A: Given the integral  I = ∫cos3(x) sin4(x) dx cos2(x)=1−sin2(x) I = =∫cos(x)(−sin4(x)(sin2(x)−1)) dx…

Q: Differentiate xcos(2x+3y)=y sinx

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Q: Determine the concavity of y = 3 + sin x on [0, 27

A: Given that y=3+sinx on 0,2πTo find : concavity of function Solution : if y''=d2ydx2>0 then…

Q: Calculate using integration by parts: x^3 sin(x^2) dx

A: Given: ∫x3sinx2dx

Q: Solve using integrable combination technique only: (x^2y^3−(6+1)y)dx+(x^3y^2+(9+1)x)dy=0

A: Solve using integrable combination technique only: (x^2y^3−(6+1)y)dx+(x^3y^2+(9+1)x)dy=0

Q: 29. (csc x – sec x)(sin x + cos x) dx find + In 5 ) dx 30. 3 sinh .3 2x3 V1 + x² sin x dx 32. 31. dx…

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Q: find the area of the shaded 4) reglon y = 2 2- y = 2 sin(Tx) 3 х -1- -2+ -3+

A: From the given graph the shaded part is on the interval x=0.5 to 2.5.  So find the area between the…

Q: 3. S sin(3x) cos(5x) dx

A: To evaluate: I=∫sin (3x) cos (5x) dx

Q: Integral of sec^4(3x) dx

A: Given ∫sec4(3x)dx

Q: Find

A: