Evaluate the following : e#/2 (a) sin(In 0) dê.

Q: Determine the value of f(z) = e*cos y+ ie*sin y at z = In 4+ Ti/6

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Q: Prove the following Sin hZ=0

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Q: Use the method of substitution to evaluate 2x cos x2 dx. sin x? + c 2 - sin x? + c sin x? + c - sin…

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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: (p² –1)cos[cosh (In r)]dr

A: In this question, we need to find the integral.

Q: Determine the value of f(z)=e*cos y+ ie*sin y at z = In 4+ Ti/6.

A: For a complex number, z=x+iy , x is the real part and y is the imaginary part .

Q: 59. Find (a) {e-t sin? t},

A: Let's find.

Q: Compute -i + cos -i sin a - sin a + i cos a where a E (T, ).

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Q: Prove the formula eix cos(x) + i sin(x) %3D Use this to evaluate e2i

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Q: Express the given quantity in terms of sin x and cos x. Sin (2n – x)

A: The given quantity is  sin(2π-x)

Q: S cos“ xdx = sinxcos² x + sinæ + c Select one: O True O False

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Q: + C,? What should be the value of A so that f A : sin (6x²) dx = - cos(5x-) %3D 4 A. x С. Зх В. 2х…

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Q: Substitute the expressions for u and for du to write tan(5x + 8)dx in terms of u. tan(5x + 8)dx = |…

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Q: 8 Find the anti denivapine Sfa) faa or © f la) = Cos ( 6x) 16 - Sin? ( 6x)

A: f(x) = cos(6x)16-sin2(6x) ⇒I=∫f(x) = ∫cos(6x)16-sin2(6x)dx Since dsinxdx=cosx, therefore:…

Q: 2. If tan 0= x2, which of the following is correct? Defend your answer. a. cos e = 1/V(1+x^4) b. sin…

A: As per the guidelines I can solve only one question

Q: Let x be real, what is the value of sin(2Cot^−1(1+x))

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Q: Find an equivalent expression to sin (z + 3)

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Q: A certain substitution gives S sin³ x cos" x dx = S(u7 – u5) du. What is n?

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Q: How would you evaluate f cos?x sin x dx?

A: We need to evaluate, ∫cos2xsin3xdx

Q: (a) sin(rxy) = x + y?

A: I am going to solve the given problem by using some simple caculus to get the required result.

Q: the solving for equa tion ty=o is 1-y= COSX %3D 2-y= Sin x %3D y= tax

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Q: O Find the anfidanialtiner Sfaw da for fla)= 18 Cos (6x) 16- Sin? (6x) © fa) = ¿* (, +x) 9 + xe

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Q: es (or+.1). COS Using P, (x), eshimate cas

A: In the question it is provided a function fi=cosπ+i The objective is to estimate the above function…

Q: help!

A: Refer to the question, we need to sketch the provided function.

Q: O Find the inde frinite in tgal 曲 A cos (2¢) df

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Q: Using an appropriate substitution, f sin (x)cos (x)dx is equal to:

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Q: c) y sin 53x =

A: Given :y=sin53x

Q: What is the value of sinh (In 2 +i)?

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Q: FIND SIN' A WHERE A= at b

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Q: Compute the following. S3x?cos(x³)dx

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Q: Solve for the convolution of sin (t) and cos (t).

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Q: expand the formula for sin(A+B)

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Q: 16. Determine So sin x cos x dx

A: First simplify then integrate

Q: find the exact value cos151ocos1o + sin151osin1o

A: We have to use cosAcosB+sinAsinB= cos(A-B)With A=151 and B=1

Q: Evaluate 3 cos z sin" e dz.

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Q: The numerical value of sinh(In 3) is equal to Select one: a. False b. True

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Q: Given that (-) x sin-1 -1 = COS eya. dy in the terms of x and y. dx Find

A: Given: xsin−1⁡1y=cos−1⁡eyx Since, dsin-1xdx=11-x2 and dcos-1xdx=-11-x2

Q: (b) If y = sin (m sin -x), find the value of (yn)o .

A: (b) Given that y=sinmsin-1x

Q: S= dx 3+ sinx+cos X

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Q: Evaluate the following: 1) f sin x sin(cos x) dx

A: Integration

Q: Using a suitable substitution, (sin x cos“ x) dx can be 4 (A) - f u*du (B)

A: Given: ∫0π2sinxcos4xdx

Q: y = C, sin at + C2 cos at, (a not to be eliminated)

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Q: sin sin ³ O de *と

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Q: The numerical value of sinh(n 3) is equal to Select one: a. False O b. True

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Q: Evaluate the following: 2Tt sin x cos x dx a) S"Isin? x cos x| dx 0. b)

A: ∫02π(sin2x)(cosx)dx Let u = sinx du = cosxdx ∫02π(u2)du u3302π = sin3x302π sin32π3 - sin303  0

Q: Evaluate the following 2 sin (x) -dx 1+ cos (x)

A: I = ∫0π/2sin(x)1+cos(x)dxI = ?