Q5. If coshx = csc20, prove that 0 = n+ cothe¯. [Hint: use identity sin(2a + 2n)] %3D

Q: The suitable substitution to evaluate the integral tan (2x) dx is 4 C cos“(2x)

A: Explanation: Given that, ∫tan52xcos42xdx

Q: If x = t + 2 sin(at), y = 3t – cos(nt), evaluate at t =;

A: Given that x=t+2sinπt, y=3t-cosπt, we have to find dydx at t=12. Now, dydx=dydtdxdt…

Q: Q4 Evaluate the fo ng In10 1- 4sinh? () dx 4 2 cosh(tane)sec20d0 - 4. 0rions in term of

A: (1) To evaluate: ∫0ln 104sinh2x2dx Let I= ∫0ln 104sinh2x2dx We know that 2sinh2x = cosh2x-1

Q: ON REDMI Y3 AL CAMERA - veifhy coucly's is Theorem for the function C) 3 Cosh(z+2 where C is the…

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Q: The approximation of I = tanx dx using composite Simpson's rule with n-5 is: O 0.6165 O None of the…

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Q: 2, Sove the Following Riccati equâtion dy 2008?x- Sin?x +y? %3D 2 cosX

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Q: 5. Demonstrate the following identity: Ecosnt : cosme sin (m+1)0 sin n=0

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Q: the area outside r = 1 and inside r = 2 cos 0 is

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Q: +tlnt +tInt If x=sin and Jy= = cos prove that y"=c constant +eco te'

A: Given: x=sint2+tlntt4+etcost and y=cost2+tlntt4+etcost

Q: e Suppose flx) = Sin (x) For which value %3D of a, osas T, will f'la) = 0.

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Q: O! Find tue indefinite integrel by q meleing tue febstelion d=4 Sin o. 2 *7 16-x"

A: To determine: by substituting x = 4sinθ

Q: The coefficient of sin(x) in the antiderivative of Flx)=(cos() is 15/32 (use fraction form not…

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Q: If f(s)=sinh(s)^13 cosh(s)^10 , find f'(s)=???

A: We have  f(s)=sinh13(s)*cosh10(s)   We have to find its derivative…

Q: Find the value of the positive integer A so that: In A 1 sinh x dx 4 Jo

A: ∫0lnA sinhx=14 coshx0lnA=14 coshlnA-coshln1=14 coshlnA-cosh0=14 coshlnA-1=14 coshlnA=14+1…

Q: O Approximate So In (3 + sin x)dx using Simpson's Rule with(n = 4 %3D

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Q: let Po)- tar'c) + tant (L). show that Plx)=C,where cis a constant and then Aind C

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Q: @ If sn@ , oinqundant IL, finel He acud value for Guadant II, find Hhe accict Cor o = %3D Cas lo-)=…

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Q: Find cosh a In(sinh r)dr.

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Q: The suitable substitution to evaluate the integral V tan (2x) dx is cos (2x) COS

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Q: Which of the following is equivalent to / Isin(Inx?)]²dx , sin(Inx 14) dx A sin2(Inx 14) dx O (sin…

A: Given that, The given integration is following, I=∫[sin(lnx7)]2dxx We have to find the equivalent of…

Q: Use the given substitution to evaluate the integral.

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Q: Evaluate the following double integral sin (y) dydr

A: To evaluate the integral

Q: that y?=x+ sin Cxy) - T 2 and let ß Be the value of dy evalwated atlxy

A: Given- y2=x2+sinxy-π24 To Find- The value of dydx at π2,1 and considering that value as β and then…

Q: The integral ·S= dx (x²+4)² can be transformed to which of the following when trigonometric…

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Q: a2z a2z dz Q3) A: If e-(sinx + cosy), show that ax2 ду? at

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Q: DIfferentiate the following fuh ction with respect to K In X %3D Sin a

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Q: Find the largest interval on which the following IVP has a unique solution. (2t + 1)y" + sin t y…

A: NOTE: Refresh your page if you can't see any equations. . to find the undefined point take…

Q: Q2// Given that oc= = sec-(-V13/2), find sin x, cos x, tan ox, csc o and cot x.

A: Given: write as Formula used

Q: Find S z? sin z dz

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Q: Use D'Alembert's formula to solve the following (IVP): Utt in R x (0, 0) | u(x, 0) u(x,0) = sin (x)…

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Q: Evaluate the following integral. sec c 2x tan 2x dx

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Q: S-) Find the gereral solufon of Sin'x y"- (2sinx.cos x)g'+ Ccosx+1)y = Sih? x given that y-sihx and…

A: Given differential equation is sin2xy"-2sinxcosxy'+cos2x+1y=sin3x Here, qx=sin3x Given that y1=sinx…

Q: Find dr/dθ in sin (rθ) = 1/2

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Q: Which of the following equations is equal to 1 @ conh (x) – sinh?(x) ® tanh (x) – sech (x) C) coth…

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Q: 22: Find dyldx for the following functions * (40 marks) · y = In (3 – 4 cos x) + (4x – 5)5 2. y = x²…

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Q: sin $ 3 y cos*3 ydy

A: We have to solve above integral

Q: Evaluate integral S (2 sin a + 4 cos z) dæ

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Q: Find the tayler seris of f(x)=cos(x+pi/6) centared at a=pi/3

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Q: Use the substitution formula to evaluate the integral. 27 3 cos2 x sin x dx 1/3

A: Given that: ∫π/32π3cos2x.sinxdx

Q: (a) Use the definitions above to show that d tanh x dr 1 cosh r

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Q: The approximation of I = tanx dx using composite Simpson's rule with n-5 is: O 0.6158 0.6165 None of…

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Q: csch(3 tan x) + sin² x cos² x dx

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Q: 27n 4 cos x sin x dx 7/3

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Q: dy is let y = cos(In(cos(x))), then da

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.