tan (x) = 7.1. If x and y are complementary, what is cot (y)? %3D

Q: Solve the given diffential by variations of parameters 1. y" + y = cos x

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A: The formula of integration using by parts:       ∫fg' =fg - ∫f'g

Q: dx a sin x+b cos x

A: Given problem:-

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Q: (5an 20 elan 20 sec²2 Bd ß 1. e?x +2e* dx e* +1 2.

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Q: The change in heat radiated by a body, detected by a pyrometer (non-contact temperature sensor), is…

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Q: 5 sin?(t) cos“(t) dt

A: ∫0π5 sin2t cos4t  dt=5∫0πsin2t. cos2t .cos2t dt=5∫0π sin2t ×1sin2t cos2t dt=5∫0πcos2t…

Q: Find the antiderivatives of e* sin x. 3.

A: Consider the given function.The given function is,

Q: 39 Find 3+e" - dx. a) b) sin' xcos x dx

A: Given that:                               (a)∫013+exexdx(b)∫sin2x.cosxdx

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Q: 1. cos? 2t dt

A: Given query is to eveluate the integral.

Q: d 1. Find (esin(x)+cos(æ)) dx

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Q: e Cos xdx

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Q: a) Given that y= sinh'(cos(x)), provide detailed derivation to obtain the expression of dx

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Q: Differentiate: y = cos(5 e* ) e11 COS

A: Ans is. option a)

Q: Question 4. Show that the average value of f(x) ei. = e- + cos x on the interval [-7/2,0] is

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Q: dx A. 1+cosx

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Q: cos(6 x) dx = %3D

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Q: ю 2ах—х e la dx Use gamma or beta laws

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Q: Evaluate each definite integral.

A: To evaluate the given integral. a. ∫01e-xdx Solution: ∫01e-xdx=-e-x01=-e1+e-0=-e+1=1-e Therefore,…

Q: y = In tan(x – A) +B

A: Some Important Formulas 1. ddxtanx = sec2x2. ddxsin-1x = 11-x23. sec2x = tan2x +1

Q: 2ах — х e la dx Use gamma or beta laws

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Q: L{cos 5t} OS

A: To find the laplace transform of cos2 5t. We use the cosine formulas to solve the given question. We…

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A: I understand that we need to find the derivative of this function as nothing is mentioned

Q: S Si dydx %3D 1-r

A: To evaluate the given double integral.

Q: 5) [ e sin e dx

A: Topic = Integration   As per guidelines , At  a time only one question can be answered.

Q: f (x) = csc(cos(e*+1))

A: We have to find the derivatives of given function: fx=coseccose5x+1 We know following derivatives…

Q: The integrating factor of the LDE y =x-2ycotx is A cos?x B sin3x © sec?x D csc?x

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Q: e 9. cos(x) dx - " sin(x) dx. Evoluate

A: Formula:∫ cos x dx = sin x + C∫ sin x dx = - cos x + C

Q: b) L{e" sin(3t)}

A: b) We need to evaluate the Laplace transform of the following expression e2tsin3t

Q: Find the value of -4t e cos(4t) dt.

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Q: 6. S sin*(e³*) cos(e³*) e³× dx

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Q: i. S(e** cos(2x)) dx

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Q: find dy for ee Sin (メ+34) dx

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Q: (ii) Evaluate J dx. COS TI

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Q: cos'x sm'e dx

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Q: 10. cos (1/) dx

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Q: | (3e* + 1)? e* dx

A: Given integral, ∫3ex+12ex dx

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Q: d dx et ex sin x + e* cos x

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Q: If y= cot"+ tan-1x?), then dy dx x2 Select one: 2х + 1+x*' 1-x4 2x O a. 2x O b. 1+x' 1+x? 2x Oc. 2x…

A: All given options are wrong. See the attachment

Q: COS T dx sin' a

A: given that a integration we solve by using integration method . Here i attached solution of this…

Q: d) cos (5æ) cos(7r)dx e) S tan e sec“ rdr

A: we have to find the following integral