13. Evaluate using the substitution u = 1 – x² or trigonometric substitution. (b -ак х (a) dx x4 (c) (d) dx VI-

Q: ду Let y = In Vx² + 2z3 + cos(b³), find

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Q: 1 2. Evaluate =dx using the trigonometric substitution x= 2 tan0. 2 Vx + 4

A: As per honor code, we will answer the first question for you. Please submit the other as a separate…

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A: We have to prove the given differential equation to be true.

Q: d (arccot(x)) -1 Be sure to provide a written justification for 5. Prove your work. dx 1+ x2

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Q: (b) (cos(x) (2x + 3))'

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Q: dx- B- If y = cos*x – sin*x , prove that: - d²y = -4cos2x dx²

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Q: 28+1 b:If y =-1 prove that. 1- 2y dx

A: # we are entitled to solve one question at a time, please resubmit the other question if you wish to…

Q: The x2- 4 dx can only be evaluated using trigonometric substitution technique . A True B) False

A: To find if the given integral can be solved only by algebraic substitution technique.

Q: x³Væ² + 1 dx

A: Solve the integration

Q: The x² – 4 dx can only be evaluated using trigonometric substitution technique . A) True B False

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Q: The approximation of f, xin(x + 3) dx using two points Gaussian quadrature formula is:

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Q: Evaluate the integral (Trigonometric Substitution) 1 (b²y6 - y³)żdy

A: Given integral ∫b2y6-y812dy The objective is to evaluate the integral by trigonometric substitution.

Q: Find Duf at P. 3 4 f (x, y) = sin(3x – 4y); P(4,3); u = i j %3D - - NOTE: Enter the exact answer.…

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Q: pin z +y 12 + cos 2 2r F(1,y, 2) =- TY + 2,- + Cos 2

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Q: sin(nz) b) E: on (0, 2x] n-1 AcoAnA

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Q: (sin 2x)y' = y cos 2x

A: Consider the given Differential equation, sin2xdydx=ycos2x divide both side of the differential…

Q: (10) The result of (D-3D D, +2D;)sin(x-2y) is

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Q: 8- Evaluate a) Sz? + 4 sin(8z) dz 1+9cos(8z) бх- х2 b) S 3x. csc² dx x3-9x2+8

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Q: Evaluate the integral (Trigonometric Substitution) x*dx (x² + 1)²

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Q: (a) If y = xV², then dy dx (b) If y = (2 + sin 3x)", then d (2 + sin 3x)" = T(2 + sin 3x)=-1(cos 3x)…

A: We have to differentiate the given functions: a If y=x2, then dydx=2x2-1 b If y=2+sin 3xπ,then…

Q: 5. If y= tan x, prove that y``=2(1+ y² )(3+ y²).

A: Prove the given equation

Q: Evaluate using the substitution u = 1 − x2 or trigonometric substitution.

A: Given: ∫x1-x2dx  ……1

Q: 8- Evaluate a) ſe² + 4 sin(8z) dz 1+9cos(8z) бх- х2 b) J 73-9x²+8 esc²) dx Csc2 - х3-9х2+8

A: We have to use proper substitutions.

Q: If f(x,y,z)=In(x²y+sin² 12

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Q: In y = C, sin 8x + C cosax + 9x²- 2

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Q: 10. Given that 2y- sin 2x =0 and y = 0 when x 0, then y?= %3D %3D dx B. 1-cos 2x C.-2 cos 2x A.…

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Q: g(x, y) = 9x sin(x²y) Calcule 9ry

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Q: a2f Compute Je Je дх' ду f(x, y)= x²y² – sin 2 + xe" and : дхду

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Q: dy 2 3 ...2 C05X +sinx...y.-(4x+5). y. ---

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Q: 5. 2 sin7 0 cos Od0 )dy 1 6. JF(ylny 9-y².

A: Use the method of substitution to solve a given problem.

Q: Q.2 Find [(x' +5x² – 2) sin 2.xdx . c Inx

A: According to Bartleby Q&A answering guidelines I can answer only one question

Q: 6xsec 3x 2-If y = (tan3x)²² prove that = (tan3x)²= + 2ln(tan3x) %3D dx tan3x

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Q: d 1 - (sec-!r) = dx Prove that xVx - 1

A: Let y=sec-1xsec y =xcos y =1x.....1 Thus sin y=1-cos2y=1-1x2=x2-1x2=x2-1x .......2

Q: 3. Show that: • T/2 sin" x dx • T/2 cos" x dx

A: Recall the property of definite integral:

Q: State the trigonometric substitution appropriate to the integral: fx*(x² - 16)² dx 3/2 | A. x 16 sec…

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Q: (4D3 + D)y = e2* A. y = c1 + c2 cos 0.5x + c3 sin 0.5x +e2x 33 B. y = c1 + c2 cos 2x + c3 sin 2x…

A: From the given problem: 4D3+Dy=e2x The auxiliary equation is: 4m3+m=0m4m2+1=0m=0  or…

Q: 8 cos (2r² + 2y²) dy dr Hint You could take a cab to the pole.

A: Given the integral is ∫02∫04-x28cos2x2+2y2dydx

Q: I Eliminate the arbitrary constants y = C,e -2x COs 2x + ce <-2% SIn 3X

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Q: dy is: If y = tan(47x²) then dx

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Q: What is r = -12 2 cos 0-7 sin e 2y - 7x = -12 in Cartesian form? x² + y² = -12 2x-7y

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Q: d (cos² 2x)=-2sin 4.x dx 12 Show that %3D

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Q: Find Duf at P. 3 4 f (x, y) = sin(x – 5y); Р(5, 1); u = i и %3 - - NOTE: Enter the exact answer. Duf

A: This is a directional derivative problem

Q: Express = In(4t), y = 7 – t in the form y = f(x) by eliminating the parameter. y =

A: Given equation is as below: x=ln(4t)y=7-t

Q: If y= tan x, prove that y 2(y² +1)(3y² +1).

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

Q: z = 3e*jS, y = 3z2 + sin(z) iS l5 al: Jis dx

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Q: 1. If y= tan x, prove that y= 2(y´ +1)(3y² +1).

A: Use the following differentiations as, ddx(tanx)=sec2(x)ddx(sec(x))=sec(x)tanx Now, differentiating…

Q: Q# (17' Compute: [tan (10x)sec(10x)dx tan³ 1 tan(10x)+C 10 1 A) tan (10x) – 3 30 1 1 В) sec (10x)--…

A: We use substitution method to solve the Integral.