2)( L[ (1 – 27)' sin 2r.dr)) =

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A:

Q: 1- Differentiate. a- Y= 2 e2+1 b- Y= -2 sin?x c- Y= 3sin2x - cos 4x d- tanv(1-x)

A:

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

A:

Q: 4. Show that sin(0 – ø) R2 – 2r R cos(0 – 4) + r² dø = 0. -

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Q: sin 3t dt J cos 3t – 1

A: Given: I=∫sin3tcos3t-1dt   ....(1)   We know that; ∫1ax+bdx=1alnax+b+C And ∫a·fxdx=a·∫fxdx, where…

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

A:

Q: 3) Prove that c) cosh2x = 1 + 2 sinh? x

A: In the question we have to prove the given function.

Q: 5. Evalvate the Intgral S2 cos (2x) - Sin 2x)=

A: To evaluate the integral: ∫2cos22x·sin22x dx Solution: We know that, 1). 2sinθ cosθ=sin2θ 2).…

Q: V. Show that: 1. [(cosx-sin x)'dx = x+ cos 2x +C 2.

A:

Q: 4) a²y=+52y =14 yat (2,1) Find equátion of tangent?

A: Equation of tangent  y-y1=m(x-x1) (x1,y1)are the points at which equation of tangent is to be…

Q: 4. Evaluate sin (44°) + COS (290) using differentials. Refer to special triangles.

A: To evaluate  sin440+cos290 using differentials.

Q: Find the differential of z = sin²(5x) + ev

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Q: of cos 2 2 sin 0) de has the form 1 -F 4 sin lue of 0 to make F(0) =0?

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Q: 1- d/dz [cosz] = -sin z

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Q: Integrate with respect to x: sin(3r) b 2 cos(4x) cos²(2x) a

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Q: 3. Show that sinh a + sinh y = 2 sinh cosh %3D

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Q: 2 sin 2x dx Tcost x + 4 cos² x – 2

A: We will answer the first question since exact one was not specified. Please resubmit the question…

Q: (27 (b) Show that 0. 4 tanh- 2x dx In 8. 16

A:

Q: (b) Show that 2t cos x and sin x = 1 + ? (c) Show that dt dx 1 +

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Q: Compute*cos(Inx)dx. 1 A.-—-e (cos1-sin1) - 2 2 1 B.- e 1 C.-e TT 1 2 e

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Q: 8. y = In(2e-t sin t)

A:

Q: If xy-In(3 sinh(3x)) , then x? y'-

A: Given,           xy=ln3sinh3x

Q: (2) If y = (sin-1(x))², prove that (1- x2)y" – xy' - 2 = 0.

A: here first we will derivative with respect to x then squaring both side and put value of the y then…

Q: 3) Show how the substitution u = 2 x shows that - - t/2 -Tt/2 S sin"x dx = S? cos"x dx

A: Let u=π2-x Differentiating u w.r.t. x- dudx=-1du=-dx Considering left hand side of the given…

Q: 3. J sin53x dx. 4. J tan 2x sec22x dx.

A: ∫ax+bn dx=1aax+bn+1n+1+C

Q: 10. J(3x3 — 5х + sin3x) dx -

A:

Q: V3 with 0 < x < 2n. 2 cos 2x cos x – sin 2x sin x - -

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Q: Show that sin(x^2) ≤ sin x for 0 ≤ x ≤ 1. Deduce that sin(x^2) dx ≤√2/2 on the invterval [0, π/4]

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Q: Find the definite integral of ƒ™/* cos 3x sin 5x dx. -π/4 Option 1: Option 2: Option 3: Option 4:…

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Q: Cos 5x dx 3 +Sin 5x 1. 2. dx J16-9 (n x)²

A:

Q: 2- y = prove that (sin x) = cos x %3D dx

A: Topic:- derivatives

Q: 2. Use the substitution technique to find [*5'sin(5¹) dt exactly (not an approximation).

A: The given integral is ∫015tsin5tdt use the formulas, ddtat=atln(a)∫sint dt=-cost+C

Q: .2 1 2x -1 Prove that : sin .2 dx = 72 1+x 1+x?

A: Solution of given question is given step by step

Q: dx 1 + sin(ax) %3D

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Q: S cos (2x) sin* (2x)dx a.

A: Solution: The objective is to evaluate the integral

Q: 4 sin' 2x cos 4x dx 4.

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Q: The answer of integ ra Ssinzx cos3% dX

A: We have to evaluate the given integral.

Q: 4) z = (4 + j3)sinh(3+j)+cos(3-j2)

A:

Q: 15. -- sin(2+ 2) dz

A: According to the given information, it is required to solve the give integral.

Q: 1. / cos" (2t) sin² (2t) dt

A: 1.

Q: 4. Evaluate sin (44°) + + COS (29°) using differentials. Refer to special triangles.

A:

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

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Q: 2 2 sin (2t) dt. 8 - cos (2t)

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Q: sin³€ dt to ylomeldon 3.

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Q: 3) e4x = sin(3x + 4y)

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Q: 4 sin (In t) cos`(1nt) dt 5.

A:

Q: 6. Vsin x sin 2xdx Vtan 4x 7. J cos² 4x 8. cos 2xsin 2.xdx |arctan(3 – x) - dx 9. 1+ (3-х)? 3e 2y…

A: Given