2 Z = 31 + (Sin 28 + ((ase Ÿ -(Sin@) Fined Iz1 12

Q: The value of 1 cos (tan ¹y) + y sin (tan¯¹y) cot (sin¯¹y) + tan (sin¯¹y) is......... +y¹

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Q: 1 Show that L-1{ = (sin hat sin at) s4+4a4, 2a²

A: It is given that, L-1ss4+4a4=12a2sinhat sinat. A partial fraction decomposition of ss4+4a4:…

Q: Use TWO different methods to find the PS of the IVP: sin x + y cOs x = 0 ( y(7/2) = 2020

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Q: 2. Solve: sin 3x dr + 2y cos 3x dy = 0

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Q: Show that (1-)dy+(cos xsin x-sy")dr =0 is an exact equation. Hence, find its general solution. Hint:…

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Q: 5. S(sin3x + cos2x)²dx

A: To find : ∫sin3x+cos2x2dx

Q: Evaluate sin (44°) + cos (29°) using differentials. Refer to special triangles.

A: To evaluate sin44°+cos29∘ using differentials.

Q: find the volume of the solid

A: Find volume of solid.Sketch the given function.

Q: y" + y = 3x sin x

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Q: Show that L-1{ = (sin hat sin at) s4+4a4, 2а2

A: To find Inverse Laplace transform of ss4+4a4: write ss4+4a4 as  ss2+2a22-2as2 Then the denominator…

Q: 38. Differentiate y = 2 cos² - a. – sint b. - sin 2t C. - sin - d. sin-

A: Differentiate y=2cos2t2

Q: 15. cos³ 3x 3√√/sin 3x dx

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Q: | sin(4z) cos(7z) dz.

A: To find:∫sin4zcos7zdz

Q: f/² sin (1) 4x ; (**) sin (²) COS (²) dx (Consider initially the first 2 terms)

A: ∫vn dv =vn+1n+1+C

Q: Evaluate dy/dx at the point (π/2, π/2), if 2 sin^2 x + 1/2 cos y = (3 sin x)^11 . Mention all…

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Q: 7 Express cach of the followir giving only principal values: (a) sin (2 – i)

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Q: 5. Find y', if y = 2cosx sin2x – sinx cos2x %3D

A: NOTE:according to company rules I need to solve first question when multiple questions are posted

Q: 3 (4+sin-15x)° dx (8) V1-25x2

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Q: dt cos (2 sin 21) /1– 4r

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Q: find the value of so that ky"=-1 at y=. 6. For cos x- sin y=-

A: On solving this by doing differentiation implicitly we get

Q: 5. Find y', if y 2cosx sin2x – sinx cos2x %3D

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Q: 3. Find S sin5 x cos* x dx.

A: Use substitution method

Q: 3. sin 3z cos 5z dr

A: Here we have to evaluate I=∫sin3xcos5xdx

Q: 7. S sin3 4 x cos5 4 xdx

A: To find the integration

Q: Find cos(4x) sin(4x) da.. To cos(4x) sin(4x) dx : =

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Q: (2 cos 2x+ 3 sin 2.x) 7. evaluated at x = 1 rad

A: Given query is to find the value of the expression at x = 1.

Q: Š 4 sin(3t) 2+ cos(3t) 7 sin(3t) + dt (2+ cos(3t))²

A: Definite integration

Q: 4 cos () dx 10. x³ sin3

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Q: 12) Given y = 2 sin2x Period = b 3D Period = 1-- -1- -2

A: Solution: Give y=2sin2x Now use the form [a sin(bx-c)+d] That implise a=2 and b=2   Period =…

Q: sin $3xcos 3x dx

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Q: Solve: sin 3r dr + 2y cos 3r dy = 0 %3D

A: First make the differential equation in seperable variable form, that is taking function of x with…

Q: .15 S sin²4y cos>4ydy

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Q: 2y 1 + cos 3x - 4.x + 3y sin 3.r = 0 %3D dr

A: 2y-1x+cos3xdydx+yx2-4x3+3ysin3x=0 Rewrite the above ODE in the form of Mdx+Ndy=0.…

Q: 3. x = 2 cos(3t) – 4 sin(3t) and y = 3 tan(6t) at t = 2

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Q: _5. In the equation y = sin-1 x, if = , then y= TC %3D %3D %3D

A: 5. In the equation y=sin-1x , if x=12 , then y=π6. The given statement is True, The reason regarding…

Q: In=5 dx Sin^ (x) ( ategrate by parts for findu the Yreduction form (11) by using (i) find In and…

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Q: sin 2t cos 2t dt 1 +3 cos 4t

A: Integration is the process of finding the anti-derivative function of the given function. The…

Q: 1. / cos" (2t) sin² (2t) dt

A: 1.

Q: 1. sin (3z) cos5(3z)dz

A: Note -  Acc. to Bartleby guidelines, we are supposed to do only one question . If you want more to…

Q: 1. f/² sin (1) cos (4) Sir sin (²) dx (Consider initially the first 2 terms)

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Q: "+25y 4r sin(51) – 2e" cos(5t)

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Q: If siny=x^2 Then find the value of cos2y

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Q: 8 sin(2x) cos(2x) dx

A: We have to evaluate the given integral

Q: (7) (4+sin-15x)° dx V1-25x2 3. dx (8) J Ja +x Vx

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Q: * /2 2 sinh (sin 0) cos 0 d0

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Q: . Evaluate S sin' 2x cos 2x dx

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Q: 4x – 1 for the 2 tan(4x-1)-3 cos² (4x-1) dr. what will be the resulting integrand? If we let u =…

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