Integrate using the method of trigonometric substitution. Express your final answer in terms of the variable x. (Use C for the constant of integration.)

Q: 3 dx (1 – x)? - A 3 В 2 D 3 E divergent

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Q: Sxe*dx Use integration by parts and simplify your answer. ex — хе* + C x + e* + C >>>> x - e* + C…

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Q: Solve this differenttial equation.   By help of integrating factor. (3xy+6y^2).dx+(2x^2+9xy).dy=0

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Q: (sinx)" dx is:- 4) The solution of (sin x) dx A) (sinx)' dx B) C) Zero

A: ∫0πsinx7dx=∫0πsin7xdxWe know…

Q: Which constant c would best be described as a constant of integration? c +1 Secx=a

A: The indefinite integral always results a constant of integration.

Q: Integrate the following expression, and solve for the constant of integration using the fact that y…

A: To solve for the constant

Q: x? -dx ² 2 Integrate by trigonometric substitution: V7 -x

A: We have to find the integral

Q: d) fe'cos( 41)

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Q: 1 of x only, then = 0 (x) dx ne given equatio 2 21

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Q: Solve the ODE by finding an integrating factor for exact equations. (2xy2+3x)dx - 2xydy=0

A: Recall: If the equation M(x,y)dx +N(x,y)dy=0 is not exact and ∂M∂y-∂N∂xN is a function of x only…

Q: Use undetermined coefficients method to solve b. y" – 2y' + 5y = e* cos 2x %3D

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Q: dx Integrate by trigonometric substitution: .2 4x² -9 2

A: Given integral :

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: noose a non-exact equation and solve. (xy - 2y?)dx - (x2 - 3xy)dy=D0 1. 2)

A: Q(1)  We have to solve given non exact differential equation:

Q: Find an integrating factor and solve the given equation. (12x + 3) + (4²+¹2) = 0 12y dy dx

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Q: Determine whether the statement is true or false. LL I 8x2 sin (x - y) dx dy 8x2 sin (x - y) dy dx…

A: The limits of the variables are given as : 0 < x < 2  &,  - 5 < y < 7 All the limits…

Q: Using undeterminate coefficien ts, Solve : d'y _q dy =9 e + 82* dx 3 3X 3 dx

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Q: LUse the method of undetermined coefficients to solve dx 5x + 9y + 2 dt dy -x + 11y + 6 dt

A: Consider the provided question,

Q: (a) /4 1+3 cos² 1 d.x; COST dx3B

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Q: (In x)2 e. d. *dx p, 2x

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Q: e dx + (2y + xe") dy = 0

A: Given ey dx+2y+xey dy=0 Here M=ey and N=2y+xey ∂M∂y=ey  , ∂N∂x=ey Therefore,   ∂M∂y=∂N∂x is exact…

Q: 4 – 9x?dx using integration by parts and trigonometric substitution.

A: To evaluate the integral: ∫4-9x2dx Solution: Let substitute x=23sint. Differentiating both sides,…

Q: sin (tz) I = dz , c: |z – i| = 2 24

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Q: 1. [D³ – 6D² + 11 D - 6) y = cos x sin x

A: To find solution of differential equation

Q: cos a eT dx ¤ dx Csc x

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Q: CSc x e dx Cos x

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Q: / 2x/64 – x* dx Evaluate the integration by substitution 16л 4л

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Q: Q/ Solve the differential equetion (x²4)dy=zxy dx

A: As per our guidelines we need to solve only one question. Please repost the remaining questions as…

Q: d³y d?y dy dx3 dx3 - y = 4 sin x dx

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Q: Solve f (5x + 6)eª dx using Integration by Parts. Use u = 5x + 6 and v' = e".

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Q: / [cosh²(2x²) – sinh?( 21²) ]dx is equal to A B dx c) None D x²dx E xdx

A: Let's find.

Q: By using appropiate substitution, solve dy hpT i. x2 dx 1 = xy – y² ii. – 2. (2х + у)е2»+у | dx

A: Consider the provided question, (b) (i)

Q: Solve y" – 4y' + 5y = e*cosec x by method of variation of the parameter? %3D

A: Given that, the differential equation is y''-4y'+5y=excosecx. The auxiliary equation is m2-4m+5=0.…

Q: (2y² + 3x) dx + 2xydy = 0 Determine an appropriate integrating factor (x) or (y) that transforms the…

A: Solution :

Q: y (2xy + y²) dx + x (y² − x) dy = 0

A: According to question given:y(2xy+y2)dx+xy2-xdy=0y(2xy+y2)dx=-xy2-xdydydx=-y(2xy+y2)xy2-x

Q: Solve the first ODE and find the value ofC constant when y(1) 2 dy 6x + 4x + 4 4y dx Your answer

A: Ordinary differential equations

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

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Q: || dy 3. dx 5x2y and f(0) = 6, solve the separable

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Q: Solve by using Integration by parts: Show and solve for u and dv. xe?* a) (2x+1)² da dx

A: The formula for integration by parts is: Here,

Q: iven the ODE, solve: x(x + 4)*dy + [y(x+ 4)* – 3x*y³]dx = 0

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Q: y = C, e3x + 2C2 sin3x

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Q: FCH)- O -t e Sin 2t dt

A: To find the below integral. ft=∫0te−tsin2tdt

Q: B: Solve the following integrations: a- fx³e-2x¹ dx b-fdx c-f 3sec³ x. tanx dx marks

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Q: (2x2 + 3у? — 2)dx — 2хy dy %3D 0

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Q: Using the method of changing independent variable, solve (1+ x)°y" + (1 + r)y' +y= 4 cos(In(r + 1))

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Q: Test for exactness and find the general solution. (2xy – sin x) dx + x²dy = 0

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Q: Integrate dx/a^2+(x+b)^2

A: Take the substitution that x+b=t.

Q: L, 4x(1– x²)dx S 2 i) ii) -) dx ? (х + Sin?x

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Q: To integrate x3x² 842 242 Ox we apply integration by parts and in the form u dv, dv is set as: dx'

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Q: Solve for the differential

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