After a trigonometric substitution, which of the following is equivalent to dx ? ) Siócor, de (B) G cos 0 16 sin20 -1 de (C) O do d0 (E) do 64 sin 0 cos20 cos 16 cos?0 64 sin-0 cos 0 1 1 o Si6sio do (G) 16 sin-0 64 sec 0 tan- d0 (H) de 64 sec-0 tan 0

Q: 27. Inside the circle r = 3a cos 0 and outside the cardioidr = a(1+cos 60), %3D %3D a > 0

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A: Use the substitution method and integrate the given expression.

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Q: 74. If x = a(1 + cos@coso), y = b(1 + cosesin4) and z = c(1 + sine) then which of the following is…

A: Explanation of the answer is as follows

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A:

Q: S ' | Sc Sex²0 The integral dx (x²+4)² see c³0 de s²0 de csc ³0 de sin ²0 de can be transformed to…

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A: To find : y'

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A: Given query is to evaluate the integral.

Q: below - and tan e 0 3n and 플<0< 12 cot 0 =. cos 0 cos 0 =. cot 0 =_

A: If you like the solution then please give it a thumbs up... The Answer is:           Explanation:

Q: 35. The cissoids r = a sin 0 tan 0. (See Exercise 29.) Ans. sin 0 cos 0 dr - r(1+ cos? 0) d0 = 0.

A:

Q: 4. 2 sin e cos e - cos e 1- sin_e + sin?e- cos? e

A: (2sinΘcosΘ -cosΘ)/(1 - sinΘ +sin2Θ -cos2Θ ) (cosΘ)(2sinΘ -1)/(2sin2Θ  - sinΘ ) cosΘ(2sinΘ -1)/(sinΘ…

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Q: ·S= cost cose de . 1-sino sece tane de sec-1 The integral sine de 1+ cose sec²0 de 1+tano x dx can…

A: Let's transform integral by using trigonometric substitution.

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A:

Q: S= The integral dx can be transformed to which of the following when trigonometric substitution is…

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Q: Carrying out a trigonometric substitution on the integral x2- 4 dx. 25 „it is obtained that it is…

A:

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A:

Q: The following is equivalent to the choices below except | (tan (x)+ 1) dx 1 dx cos? (x) sec (x) dx…

A: Please refer the attached image for complete solution. THANK YOU.

Q: (x cos + y sin?)y – (vsin? -x cos?)* х — х COS = 0 Ans: xy cos = c (Lucknow, 1997; Kanpur, 1996)

A:

Q: Which of the following is equivalent to -dx 1+ cosx – sinx after appropriate half-angle substitution…

A:

Q: (g Suppose cos(a) = - and sin(a) is positive. 3 If the point (-2, y) is on the terminal side of the…

A: Given,           cosα=-23 and sinα is positive. Also, the point -2,y is on the terminal side of the…

Q: 1-sin e 5. r2 cos e dr de

A: According to question∫0π∫01-sinθr2 cosθ dr dθ

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A:

Q: Test the DE for exactness then solve. 6. (2xy³ + cos x tan y + 2 sin x) dx + (3x²y² + sin x sec? y –…

A: As we know that, the differential equation Mdx+Ndy=0 is exact. if  ∂M∂y=∂N∂x The solution of the…

Q: * What trigonometric substitution should be used to evaluate x² - 9 dx? x2 A x= 3tane B x= 3sine…

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A:

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A: To Establish the identity

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A: Consider m=x.

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A: To Prove: cosA1+sinA+1+sinAcosA=2secA

Q: If y=tan(arcsec /x), then dy/dx is sec?(arcsec/x) (B) none of the given choices x- 1 2(x– 1) 2(x- 1)…

A:

Q: When integrating by trigonometric substitution | V4x² +25 dx becomes a) jsc 25 sec? O tan O dO 2…

A: Solve

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A:

Q: 10. Find the general solution: (r + sine – cose)dr + r(sin 0 + cos 8)de = 0 a. r? + 2r(sin 0 – cos…

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Q: tinuous, prove that T/2 T/2 f(cos x) dx = f(sin x) dx (b) Use part (a) to evaluate /2 cos?x dx and…

A:

Q: A. 5 cos 0+3sin? 0 = 3+2cos 0 B. cos x(secx - cost) = sin? x %3D 1-2sin? 0 С. sin ecose = cot 0-…

A:

Q: dy -? If x=5+ cos20 and y=3– sin20 , what is dx A none of the given choices B csc 20 (c) -cot2ө D…

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Q: f tan(0): and sin(0) < 0, then 3 %3D sin(e) = %3D cos(0) = %3D sec(0) = csc(0) = cot(0) =

A:

Q: D^n/dx^n (e^(ax)sinbx) = r^(n)e^(ax)sin(bx +theta) when a and b are pos numbers, r^2= a^2 + b^2,…

A: Let y = eax sin bx Differentiating the above equation with respect to x we get, dydx=y1=aeax(sin…

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Q: 10. (r + sin e - cos e) dr + r (sin e + cos e)d e = 0

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Q: A Moving to another question will save this response. Question 9 The suitable substitution to…

A: Explanation of the answer is as follows

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A:

Q: Find the GS of: (r + sin e - cos e)dr + r(sin e +cos E)dO =0 O r2+2r(sine - cos©+C=0 Or2-2r(sine -…

A:

Q: 4) Sin W = %3D Cos N = W. Tan W = %3D

A: Solution: The objective is to find the required values