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Q: tan e de (1+ In cos ele

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Q: GUEN {) en: Sinx ,0s 2. COS X is equal o A O B) -4/24 c) s/24 D) 4/6

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Q: Show that sin a – sin b < Ja – b), for all a and b. (Hint: MVT) use -

A: Mean Value Theorem :  The mean value theorem states that a function f which is continuous on the…

Q: Prove that eax (a cos bx +b sin bx) + C. ax cos bxdx %3D a2 + b2

A: ∫eaxcosbxdx=eaxacosbx+bsinbxa2+b2+C

Q: Let z=x+ iy with x and y are real. What is the imaginary part of sin (x + iy)

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Q: Prove the following identity: cos³x-sin³x cosx-sinx = 1 + sinx coSX

A: We know,      a3 - b3 = (a - b)(a2 + b2 + ab) Also,     sin2x + cos2x = 1

Q: ー1 B Cos (2 oin (oen 3 + cas の An

A: Sin(A+B)=sinAcosB+sinBcosA

Q: Evaluate the following: | sinh (t) 2 + sin (cosh(t)) dt

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Q: Evaluate. fos z z sin z dz =

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Q: 2. Estimate cos (– 0.1) + cos 4

A: As per given question  We have to solve above question

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A: The given matrix is,

Q: 1. Calculate ln(-/2) and acos(2).

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Q: -2n 1 9. Evaluate : de 6+ sine

A: Given, ∫02π16+sinθdθ=2∫0π16+sinθdθ Let us take…

Q: 9. Let r = 3 sin tî + 3 cos tj + 4tk. Calculate N

A: Given r(t) To find N(t)------ unit tangent vector

Q: 10. Prove that 7/2 sin 0 cos (cos a cosec 0) do -(1-cos a). 2 ||

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Q: Let E R. Show that cos 20 cos²0-sin² 0.

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Q: 1. [* sin' y cos' ydy 3

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Q: /4 (6) Evaluate I cos y dz dr dy = A. B. C. D. A

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Q: t/2 Evaluate using Wallis' Formula: sin? x cos5 x dx

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Q: H.w Evaluate;- Cos TT lt-1)idt

A: To evaluate:  1) ∫-∞∞δt-2e-tcosπt-1dt2) ∫03∫-∞∞t2+4δt-τdτ dt

Q: dy Given y = 4e is: cosa, da Select one: a. 4e * + sinx b.-4e + sinx c. --4e¯ª - sinx d. 4e * COST

A: We are given with the function y and we have to find dy/dx which we can find out by differentiating…

Q: 7. Prove: cos(0 + 2) 7) = sine.

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Q: 27 sin? 0 27 de = (a- Va? – 62), a > |히| > 0. a + b cos e ude all the necesgary detoila rogui

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Q: 4 B C D 1 3 t ST 3 7 T 4

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Q: 3. )Find t cos 20atdt =?

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Q: xz •Evaluate So So So ²³x² sinydydzdx X

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Q: e-zusin(-u) 2.2. L e{f} du

A: Given: L∫0te-2usin32uudu To find the Laplace transform of ∫0te-2usin32uudu The formula for Laplace…

Q: 11. f sin²0 cos²0 de

A: Introduction: Trigonometric function integration requires fundamental simplification techniques.…

Q: grx) = Sin X 2. Vi+ブ× V It

A: Given     f(x)=cosx     g(x)=2sinx     k(x)=1+x