If fx is the integral t^2 dt from (x,x^2) then: f'x =  f'(-2) =

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Q: Find the solution to the differential equotion that Sotisies the quen inital condiion

A: The differential equation with initial condition is given as

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Q: Use the Cauchy Integral Formula for Derivatives to compute

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Q: Suppose a force of 40N is required to stretch and hold a spring 0.1m from its equilibrium position.…

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Q: Determine whether the improper integral diverges or converges. dx 1. (2х-1)3 dx 2. x +1

A: No.2 The improper integral is of second kind where f(x) = 1/(x+1) has one point of infinte…

Q: Integrate sin 6y sec 3y dy from limit 0 to π

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Q: 19) Derive a one point integration formula to estimate the integral f (x) dx.

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Q: Calculate the derivative ,11z d da Ja7 In (t)dt using Part 2 of the Fundamental Theorem of Calculus.

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Q: Use linear approximation or differentials to estimate the following

A: Solution: Consider the given number: 1000.033 Let y = x3 = x13 Differentiating with respect to x:…

Q: What change of variables is suggested by an integral containing V100 – x??

A: 100-x2

Q: Before integrating, how would you rewrite the integrand of S(x* + 2)² dx?

A: To solve: ∫(x4+2)2dx

Q: te dt.

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Q: Simplify down to a single integral in terms of . .3 /9-x² 63–42²–4z² Volume = 1 dy dz dx = Σ da.…

A: ∫-33∫-9-x29-x2y3x2+3z263-4x2-4z2dzdx

Q: Determine whether the improper integral diverges or converges. dx 1. (2x-1)3 7 dx 2. -1* + 1

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Q: Use integration by parts to prove the reductionformula.

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Q: Find the sdution of the. differential equation that Satisies the qven intal condition

A: We have to find solution of differential equation with given initial condition.Differential equation…

Q: 2.Evaluate the total derivative of u with respect to x for u = 4x4+3y² + 3z² when y = sinx and z =…

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Q: What is the integrable form of et dx? e-e-X

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Q: Pind the ualue of e is an integrating facko of ly-y')+xy'so

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Q: Find the set of orthogonal trajectories for r = VA sin (2e)

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Q: Find the Integration of: f(3sin t + esin ty cost dt In 3

A: we have to integrate the following

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Q: Evaluate the double integral: dy dr

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Q: Let u=sinx and the integrand will lead to integration by partial fraction

A: use substitution method for solving the  integral

Q: Evaluate the double integral [ Vy sin ydydx.

A: • Here, the inner integral w.r.t 'y' is difficult to evaluate, hence we have to change the order of…

Q: In² xdx

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Q: dx 1 Vx + x3

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Q: When is it beneficial to use the Jacobian to change variables in a double integral?

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Q: Find F '(x). F(x) = integral of 2/(x+8) dt in interval [x^2,0]

A: Let u=x^2 Then du/dx=2x

Q: (a) The centripetal acceleration of a particular wheel in a locomotive with respect to the angle…

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Q: a) by parametrizing C, b) by using the Fundamental Theorem of Line Integrals.

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Q: Does the differential dy represent the change in f or the change inthe linear approximation to f ?…

A: Given the differential is dy.

Q: Evalate the integral (tanx dx by using the reduction formıla of tangent fumction. х

A: Let u=tan(x). then x=tan-1u and  dx=tan-1u'du=duu2+1

Q: Solve the integral of arcsin(x) using integration by parts.

A: Given as

Q: Find the total differential. z = ex tan(y)

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Q: (а) The centripetal acceleration of a particular wheel in a locomotive with respect to the angle…

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Q: Find the particular integ rel of This differential etuatim. (40²+HD+= 2e +8x %3D

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Q: I Eliminate the arbitrary constants 1. X = y=at + bt² - Int,

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Q: Evaluate the iterated double integral JI-X² ( [√x² sin (x² + y²) dz dy dx

A: A a couple of imperative is a specific imperative of a characteristic of numerous actual variables…

Q: Find the the Yegion bounded by area y= tanx 4

A: integration gives the area of any function y .

Q: What is the Fourier transform of the one-dimensional rect function rect(x) = 1, for |x| |x|…

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Q: Calculate using integration by parts: x^3 sin(x^2) dx

A: Given: ∫x3sinx2dx

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Q: Evaluate the double integral. 5 25- х2 dy dx Jo

A: First, integrate with respect to y

Q: sketch , EvValuate & reverse order af integration de dy

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Q: In 3 | (1-x)e"dx ах In

A: Consider the given integral

Q: COSX - dx sin²x-5sinx-6

A: The integral is given by I = ∫cosxsin2x-5sinx-6dx                             ...........1