The appropriate trigonometric substitution for dx is V3x-x2 ww 3 X = 9 3 + sec 0 2 4 3 +sine x = O Option 1 Option 2 x - 3 = 3 sin 0 x - 3 = 3 tan 0 O Option 3 O Option 4

Q: The appropriate trigonometric substitution for * dx is V3x-x 3 3 X ==+ sin 0 2 2 sec 0 4 2 O Option…

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Q: Suppose y = sina, which is TRUE about y? 1 Oy= sin O none of the above y 0 *= arcsing O * = sin y

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Q: | cos z In(sin x)dr

A: In some cases an integral can be converted to a standard integral using an appropriate substitution.…

Q: 1 |+tan¬(x), then x2 dy If y=cot-= dx

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Q: (s,+)=(-3,1) X=5?+2+? y= 6st a) 4s x sinly) + 6+x?coscy) at (-3,1) b.) 8tx Sincy) + 6sx? Coscy> at…

A: GIVEN  (s,t)=(-3,1) X=s2+2t2  Y=6st substituting the value of s,t for X and Y we have  X=(-3)2…

Q: Show that if z = x+ iy, then: | cosh-z|2 sinh x Hint: use the equation: | coshzf = sinhx+ cos"y

A: We have , z = x + iy We know that ,  coshz = ez + e-z2 Therefore , cosh (-z) = e-z + e-(-z)2 = ez +…

Q: z = 2e"žsinx – 3e*cos(y) Ве find: www a²z a2z (n az а) дхду"") дудх ,b) ду

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Q: a tan secy dy dx Jo Q2) a) Find b) Is cos4xv2 - sin4x dx = (2- sin4x) + C true or false? show me

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Q: If rcos(x)sin(y)=a, rcos(x)cos(y)=b and rsin(x)=c, find r.

A: Formula used is written in the bracket of the first photo.

Q: By making an appropriate u-substitution, one has that sin(3x² – 2) dx = 1 a · sin(u) · du u + 2

A: Given: ∫sin(3x2-2) dx=∫a.sin (u).1u+2bdu

Q: 6. f cos¹ 2 xdx

A: Given,  ∫ cos7 2xdx

Q: Assume that a particle’s position on the x-axis is given byx = 3 cos t + 4 sin t,where x is measured…

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Q: If y = cos? x – sin? x, what is ? dx dy dy = 2(cos x – sin x) dx dx Option 1 Option 4 dy dy -2(cosx…

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Q: sin' (2t) cos? (2t) dt

A: Use the substitution and replace the terms by new variable and solve easily.

Q: 0 sin 0 Find if y %3| Vsec 0 de

A: We have to find the dydθ of the given function   the given function is y=θsinθsecθ

Q: Eliminate the parameter: I = sin 3t, y = cos 3t, 0 <t <T/3. = COS

A: x= sin 3t     and y=cos 3t     for    0≤t≤π3 We need to eliminate the parameter i.e. we have to…

Q: Q/ ind dy if 24-sini' (xe!)=sin'(x*)+ cos (x")

A: Given that      2y - sin-1(x2+1) = sin2(x4) + cos2(x4) Here we have to find dy/dx.

Q: Let x² + sin(yz) = xz² + y dz and ду dz Find

A: Given,           x2+sinyz=xz2+y

Q: sin 20 d0 J Vcos² 0 + 16 V cos?

A: Integration is summation of discrete data. The integral is calculated for the functions to find…

Q: What is the general solution of (sine – 2rcos0) dr + reos0 (2rsind + 1) d0 = 0 Orcose + r? sin² 0 =…

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Q: Given the integral sec6 (x − 1) tan4 (x - 1)dx, which of the following equations will be useful for…

A: The given integral,       ∫sec6x-1tan4x-1dx

Q: Find y' and y". y = cos(sin(90)) y' %3D %3D

A: We have to find

Q: cos“ (2x) dæ

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Q: f/² () sin cos (sin (²) dx (Consider initially the first 2 terms)

A: To evaluate: ∫0π2sinx3cos4x3sin2x3dx Let I = ∫0π2sinx3cos4x3sin2x3dx We know that  sinxcosy =…

Q: 2 2. cos² ydy 1+sin y

A: The given integration is: I=∫cos2y1+sinydy   We know the common integral. ∫sinxdx=-cosx+C

Q: Hw/ plot O r=2.2 Cose O r: 5+3 Cos e Or=l+2 Cose Or: 2. Cos O r=S-Sin 8 between 8=0 4

A: (1).  The given polar curve is: r=2+2 cos θ

Q: um point(s) for y=sin 2x- cos. d be in ovprossed in rodians

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Q: Z is a complex variable z=x+iy  question attached as photo

A: Consider the closed integral

Q: I. Differentiate the given trigonometric function 1. x = tan 3u 2. y = 4cos²y sin 4y 3. w = y+1

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Q: Evaluating ³√9-x² dx using trigonometric substitution will lead to: 15/2 A cos²0d0 B 18 cos²0d0…

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Q: dx 5) prove that sin x+c using method of trigonometric substitution. %3D

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Q: || dy tan(sin-lx) then find d.x 1. given, y

A: The given function is: y=tansin-1x To differentiate this function, apply the chain rule of the…

Q: Solve for the angle 0 where 0<0< 2n. sin 20 - v2 cos 0 = 0 0 =

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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: 1. S x4+a4 dx x3 2. Jydy √a2-y2 3. I cos2tdt (1+sin2t)4 4. I tanßsec2ßdß 5. [(tan) – 1)2d0

A: We have to find  the value of given intregation.

Q: 4 I sec(ø) (b) p* sin(ó) dpdódo

A: The answer of part b is as below.

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

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Q: 4. Use appropriate trigonometric identities to determine 1 dx 1- cos? x (i) (ii) Scos 7x dx (ii) S(1…

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Q: When using u substation what should I use as the u when the problem is the intergral of…

A: Explanation:The given integral is ∫cos3(θ)sin(θ)dθ.

Q: sin 0 cos 0 d0. Jo 0,

A: Here we to solve definite integral.

Q: 0. sin*(x) dx = R, 3 -Tt, what is 8. Given that sin (0) de?

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Q: Q7 tan (0) sec (0) de is equal to: sec (0) - 3sec (0) + C 3sec (0) +C 3cos (0) +C tan (6) sec (0)…

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Q: S sec (x-1) tan4 (x - 1)dx, which of the following equations will be useful for 1 + cos2u cos²u= 2…

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Q: Evaluate the integrals in Exercises

A: Given integral is ∫0π2costi-sin2tj+sin2tkdt

Q: Find sin' (2r)dz . - 능 cos"(2z) 글 cos (2x) + - cos (2x) + c Check your variables - y

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Q: 5. y = cos" (cot (esc V?)| - 3x)' tan x (1 6. y = 5x2 - Vcsc x 7. 2x sin y = (2x + 3y)°

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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 -…

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Q: By using Cauc hy laws find= Cos X.dx IT (x?+)) Sinx cos A) dx COS X e)

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