Find the Fourier transform 1-x, | x | < 1 f (x) = 0, x > 1 sin x Cos X CoS x Hence evaluate dx.

Q: sin* (t) – cos*(t) – cos²(t) = 1 sin²(t)

A:

Q: Show that J (x) = 2 sin x

A: By definition,                  . Now,  we need to prove the above statement by taking n = 1/2.

Q: Find dt 1- t2 sin (t)

A: Solve the integration

Q: Find the Fourier Transforms of the indicated function: f (x) = cos x e−x^2/2

A: The given problem is to find the Fourier transform of the given function. Given function, f(x) =…

Q: t' sin(2t n(21*)dt Evaluate

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Q: Evaluate (2+ it)² dt and f sin(2it) dt.

A:

Q: sin? f (x) = 피/2 |x| > T, x, %3D l리 | 피/2

A: in this question, we find the Fourier integral representation for the given function f(x)=sin2x ,…

Q: Determine if the setsin² {sin²x, 1-cos(2x)} is linearly dependent or linearly independent on I =…

A: Let B={sin2x,1-cos(2x)}.

Q: 1+sin 2 x 1) Find the derivative of f(x) %3D 2 cos3 x

A: The given function is                                    y=f(x)=1+sin2x2cos3x…

Q: d 1+ sin² (2)| dz

A:

Q: Find the maximum value of  sinx+cosx at [0,pi]

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Q: Find the first derivative of y = Arc tan √x² −1+ Arc csc x 2 O 2 O 0 2 Ox√²+1

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 1 |Leax sin(bx)] eax [a sin(bx) – b cos(bx)]+ C * Using the formula dx = ах a² + b². Sie [e-8x…

A:

Q: f(x) = 1 – sinx

A: The given function is f(x) = 1 – sin(x). Consider some values of x, find the corresponding f(x)…

Q: 7/4 (sec² x – sin x)dx

A: 1. ∫sec2x dx=tanx 2. ∫sinx dx=-cosx 3.∫(u±v)dx=∫u dx±∫v dx 4. ∫abf(x) dx=F(b)-F(a), where ∫f(x)…

Q: Show that tan-1 ( 1/v ) = π/2 - tan-1 v, if v &gt; 0.

A: To prove tan-11v=π2-tan-1v, let  x=tan-1v then tan x=v1tan x=1v Since  tanx=1cotxcotx=1v ⋯ (1)

Q: Integrate f(cos x)e*+sin xdx B. e-sinx +C A. -et+sinx + C c. ettsinx + C D. e+sinx C

A: Note:∘ddx(sinx) = cosx ∘ddx(a) = 0                                         where a is constant∘∫etdt…

Q: Star tan 5t dtl

A:

Q: compute (x2 - 8x +20) dx on the interval (0,1)

A: To evaluate the given definite integral over the open interval (0,1)

Q: tan(2x)=1 interval [0,2pi}

A:

Q: Suppose that acosx = 1+sinx prove that (a-1)/(a+1)= t where tan( A)/(2) is t

A: acosx = 1+sinx prove that (a-1)/(a+1)= t where tan( A)/(2) is t.

Q: Let f(x) = f sin t² dt. Find f'(x) x² 2x 2x sin(x4) - 2 sin(4x²) sin(x4) — sin(4x²) 2x cos(x) - 2…

A: Let .To find .

Q: Show that Sx cos*x dx = (x² + x sin 2x +cos 2x) + c

A: Given: ∫xcos2x dx=14x2+xsin2x+12cos2x+C.

Q: Prove that fx" cos(2x)dx=sin(2x)-[x n sin(2x)-x-¹ sin(2x)dx. Do not use Table Entries. H

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