Integrate the function by using trigonometric substitution. dx, x < 2

Q: "y= sint+ tant, x=-In(-cost) - esin, find the value of y when =". 4 6

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Q: . Use the I function to do the following: (a) find the value of SVxe*dx ,

A: We shall solve first question only as per the answering guidelines.if you want other question to be…

Q: (6) / zVF x² – 4 dx. Use TRIGONOMETRIC SUB STITUTION.

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Q: x² dx %3D Use right endpoints and = 10 rectangles to find an approximation of

A: Given, Use the endpoints and n= 10 rectangles

Q: Evaluate ∫x3 √(1 - x2) dx using a trigonometric substitution

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Q: Evaluate f v-8+ 6x – x2 dx using trigonometric substitution

A: The objective is to evaluate the integral using trigonometric substitution

Q: 1+x² -dx

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Q: x? dx and simplify your answer. Show your

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Q: 2.x? Evaluate dx using substitution technique. 2x' +5

A: Since Mulitple questions are asked, Hence doing only first question.

Q: /x2 (1+2х-1) 5. S dx x(х+2)

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Q: (x-7) dx 19. SJ5-4x-x2

A: Answer is following.

Q: x2 dx 16-х2

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Q: Evaluate fx sinx? dx. A. В D) Does not exist 비2

A: Given, I=∫-∞0xsin x2dx

Q: Evaluate using TrigonometriC substitution. dx 4. S (3+x+V6x)(3+x-V6x)

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Q: Csx 7. J dx 5+sinx

A: We can  solve by using Antidifferentiation property

Q: dx 17. S√4e-2x-25

A: Given integral: ∫dx4e-2x-25.We need to evaluate the integral.

Q: dx Find the value of a so that %3D 1-x2

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Q: b) f(x) = tan (VInx) %3D

A: f(x)=tan^-1(sqrt(lnx))

Q: .2 dx I (w² – 25)5/2

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Q: x*dx (x² + 4)2

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Q: 1 dx ((x+1)²–1) 2

A: ∫1x+12-12dx=∫…

Q: Evaluate x dx Sin odo 2-X

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Q: x²dx 1. J4 –x*

A: NOTE- ''As per Bartleby guidelines we have to solve only first question please repost other…

Q: sin x dxdy

A: see below the calculation and answer below

Q: Evaluate using trigonometric substitution ∫(x+4)/(x^2-9)dx

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Q: Provide an appropriate response. Find: dx Soloct ono:

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Q: 1 dx (use trigonometric substitution) x/1+x6

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Q: cosx d) s(x)

A: Given : S(x) = cosxx

Q: dx V6+x-x²

A: We need to integrate using trigonometric substitution:

Q: dy/dx of pi

A: pi is a constant.It has value 3.14 approx.

Q: differentitate the function y=(sin(8x))^x y'(x) =

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Q: 8. dx Vx² -9 2 X

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Q: The 4 dx can only be evaluated using trigonometric substitution technique. A True B False

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Q: Dsinx-sin3x [3] sin³x = find D and E. %D E

A: Solve for D and E

Q: S sinxcos(2x)dx

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Q: Evaluate using trigonometric substitution ∫1/(x^2√1+4x^2)dx

A: Given that: ∫dxx21+4x2

Q: dx 1+tan x

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Q: Salve the DE Y- 2 y'+ sy=ě sine 2X

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Q: dx e2X+1

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Q: The harmonic function is : a x? ay? ax2 ay? =10 %3D dx2 dy? =10 ду? dx2

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Q: Evaluate dx using trigonometric substitution. 25 x2 -

A: Let x = 5sinu ⇒ dx = 5cosudu∫25sin2u5cosu25-25sin2u du75∫sin2ucosu51-sin2u duAs sin2x+cos2x = 1 ⇒…

Q: Graph the integrand and use geometry to evaluate the integral. (3+5x)dx | (3+5x)dx = (Simplify your…

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Q: Perform the integration. 1. csc? x cot x/csc x – 1 dx - 6

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Q: Evaluate dx using trigonometric substitution. V25- x2

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Q: dx xVa' +x

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Q: Use the technique of trigonometric substitution to evaluate x2 dx 4 – x²

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Q: 2x dx Using an appropriate substitution, evaluate: (A 4

A: Assume 2x= t then convert the given integral into t . Use integral formulae to evaluate integral.

Q: | Vx² + 16 Use an appropriate trigonometric substitution to evaluate dx.

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

Q: dx x= 2 tane 1/2 X2VX2 +4

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Q: dx 8) x*Vx² +1

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.