4 2 |cot x| csc? x dx 4

Q: 15. y = sec'x, y 8 cos x, -T/3 < x< T/3

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Q: sin* x – 2 sin? x cos? x + cos* x dx 26. sin? x cos? x

A: SOLUTION- Since you have asked multiple question, we will solve the first question for you. If you…

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Q: P1: |x? cos-1 x dx X* cos

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Q: 13. y = cos(x), 0 <x<T

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Q: y cot x; x =

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Q: 2. Y' = csc - y cot x ans. y sin x = x + C %3D

A: We know that; The standard form of the linear differential equation of first order is: dydx+Py=Q ;…

Q: csc- x (d) | 2/4- cot? x dx xp- (e) Jx In x sec“ x (1) | (f) dx 3 tan x

A: Here we integrate the function.

Q: c) y = tan x d) y = csc x e) y = sec x f) y = cot x

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Q: (d) sin 7x dx 1 1 (e) dx sin? x cos? x (f) | (tan x + cot x) dx

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Q: 9) 2y' = y cot(x) 10) y'+ csc(y) =0 11) y' = (1+x)(l+y³) 12) yy' = 0.5 sin (@x)

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Q: 1 4. y = x² cot x x²

A: We can use the concept of chain rule of derivative in order to solve the given problem.

Q: 6 tan1 d) dz 42] =O d. [9 csc1 2y =C e) dy d. f) da 5 cot-1 4gl

A: ddx(arc cosec(x))=-1xx2-1ddx(arc cot(x))=-11+x2 ddx(arc tan(x))=11+x2

Q: 17 Find p, q if ," f(x) dx + Sii' f(x) dx = [" f(x) dx. (Give your answers as whole or exact…

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Q: y = cot х+ 2 X

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Q: x - y = x? sin x dx

A:

Q: H.W 1)ſ csc*x dx 2)ſ cot*x dx

A: #1) Given integral is∫csc4dx=I (say)

Q: r = cot 0 * csc 0

A: Given: r=cot θ×csc θ To Express: The given function in cartesian form. Formula used: cot θ=cos θsin…

Q: I+11z|10 dx=? O a. 2lna + arctan(x + 2) – In((x + 2)) + C O b. Inx? + 5arctan(x + 2) – In(1+ (x +…

A: ∫x2+11x+10x3+4x2+5xdx

Q: 5. sin x cos? y dx + cos? x dy = 0

A: As per the guidelines, we are suppose to answer only one question. Please repost the rest of the…

Q: Establish each identity.

A: To prove: cot2v2=sec v+1sec v -1

Q: Find y' and y". y = V sin(x) cos X 2 sin x

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Q: 4 TT 1 4. 2. 3 y = 1 + V2 csc x csc x + cot x P.

A: Find your answer below

Q: x². y² = x² + y? cot x y = (1+ cot x) y = In(sin 3x) y = x2. e*

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Q: y= 13 * sin x 13 "* sin x=| dx

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Q: 1 2 1 sec? nt) tan (nt Ttt ) Ttt ) dt 0.

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Q: 4. csc x dy= cot?y dx when X= T, y- %3D

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Q: Find the area of the region.

A: Consider the given parametric curves, x=2cotθy=2sin2θ          over the interval 0&lt;θ&lt;π the…

Q: h(x, y) = cos x coS y. COS x cos

A: Given that h(x,y)=cos(x)cos(y) with |x|&lt;0.1 |y|&lt;0.1 To find the second degree Taylor's…

Q: 2 5b. dx CSC X sec X (Hint : Trig. Identities) 6b. dx (Hint: Vx =x) %3D

A: The given indefinite integral can be written as: a  Let us suppose  I=∫2cscx secxdx We know that…

Q: (x) %3D 5 sec x, [л, 2л]

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Q: (х + 3) e* - dx js equal to (x + 4)? 1 +c (x + 4)² et (x + 4)² x + 4 et x + 3

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Q: 1 = | xsin(x)dx I :

A: The given integral is: I=∫x sin(x) dx

Q: 7 sin (x)cos(x)dx = + C

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Q: cos (x) – y³ cot (x)] dx 3y dy = 0 |

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Q: - sin x sin y y' cos x cosS y

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Q: cos? dx 1+ sin x .2 CoS" x 3) 6) cosh?vdv

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Q: 25. Find y" if а. у b. y = sec x. = csc x.

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Q: 1) r = 8 sec 0 2) r csc 0 cot 0

A: We know that  X=rcosΘ Y= r sinΘ r² = x² + y²

Q: ® Stan®Cx}sec®%x)dx= tan%x) , tan'(x) , tan'0) + C 10 6. 4

A: Note : “Since you have asked multiple question, we will solve the first question for you. To get…

Q: T/2 ( 4 cos (x) sin° (x) dx

A: To evaluate the integral ∫0π24 cos2(x)sin3(x) dx We know that, cos2(x)=1+cos2x2sin3(x)=3sinx-sin3x4…

Q: dx J sin?xV1- cot.² x

A:

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: d²y dy + 2y sin? x = e-cos * sin² x dx Solve : + (3 sin x – cot x) dx?

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Q: O A. sec(x) B. cos(x) C. sin(x) OD. cosec(x) OE cot(x)

A: We have basic trigonometric identities cos2x+sin2x=11+tan2x=sec2xcot2x+1=cosec2x.. . . . . . .(1) We…

Q: 7. y' = Y cot y X X

A: The given problem is y'=yx-cotyx We have to use the substitution method to solve the differential…