Evaluate dx. [Hint: First, make a substitution; then, use integration by parts.]

Q: dy xe dx to

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Q: Use order of h® Romberg integration to evaluate 1= f, x e2* dx. Compare ɛa and Eg.

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Q: Integration in REVERSE ORDER

A: Given:

Q: use a geometry formula to find the exact value of the definite integral  2x dx on the inteval [a,b]

A: As a first step let's plot the graph y = 2x and the line x = a and x = b. The line is blue is the…

Q: dx

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Q: Calculate the iterated integral. dx

A: Value of the integral is (9/2)ln2  See below the explanation

Q: Interchange the order of integration on f(x, y) dy dx.

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Q: QS-by using the double integration, find the area that lies inside the curve ra(l+cos e) and outside…

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Q: 2 dy dx Evaluate the integral: 1+Vx? +,

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Q: Sev dx (Hint: Integrate by parts with u-substitution)

A: To evaluate I=∫exdx

Q: Integration review Evaluate the following integrals.

A: To determine: the following integrals.

Q: (a) Change the order of integration and hence evaluate fo M*(ry)dydx.

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Q: Jay ti dx dy Compute the integration

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Q: Integrate: J [ xe*dx

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Q: [? sinycos° ydy 2

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Q: Evaluate | VF In(r)dx by using integration by part.

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Q: Sketch the region of integration corresponding to y²e= drdy, (log æ)3 J = and evaluate J.

A: We will evaluate the given integral.

Q: Evaluate by changing the order of integration: IL sin y³ dy dx 0.

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Q: Consider the integral æe dx: Applying the integration by parts technique, let and da = dr

A: Given

Q: Evaluate the iterated integral given below

A: The given question is from the calculus and subcategory of the double integration we can solve this…

Q: c) Seax.Sinbx. dx =? Calculate the integral

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Q: Evaluate: I = fe * x?dx

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Q: Calculate the integral: dx J (e² – 4)(e* + 6)

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Q: Integrate the followings 1 dx J (1+ )?

A: ∫1x1+x2dxLet               1+x=t             d1+x=dt                12·1x·dx=dt…

Q: оЗ Сlassify PDES below: int 3 и ди y? dx3 ue 5x ду — и + и

A: Nonlinear differential equation

Q: dx '1 x[13+ln(x²)]

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Q: Evaluat the integral, dx dy y's зу

A: We need to evaluate the double integral- ∫01∫3y3ex2dxdy Here we will use the following integration…

Q: Evaluate the iterated integral. dx dy

A: Given query is to find the indicated integral.

Q: dr 46. First make a substitution, then use integration by parts.

A: Given- ∫x5ex2dx To find the antiderivative first using substitution and then using integration by…

Q: S y sinh dy a

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Q: (a) If A  is the area of a circle with radius r  and the circle expands as time passes, find dA/dt…

A: Given: A is the area of a circle with radius r. To determine: dAdtin terms ofdrdt

Q: Integrate تلد ا - تم( فیگ S (a² – v²) * 22)* dv where " a" is constant

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Q: O Reverre the order of integration and do not ewaluate dy dx Show the region.

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Q: у? (1 — х?)dx + x(х2у + 2х + у) — 0

A: Given equation is: y21-x2dx+xx2y+2x+ydy=0 and y2x+y2dx+xy2-xdy=0 Now, solve the equation…

Q: evaluate using substitution and then Integration by Parts.

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Q: Sulve the Poll owing DiE (x'+) dy+ (2xy +) dx

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Q: cos (=) Consider S dx. Using u-substitution, determine which of the following is equivalent to the…

A: To find the u-substitution: ∫cosπxx2dx

Q: `y³e-2¥ dy

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Q: 6 dx Evaluate the integral Vr? +4

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Q: Evaluate dy dx by changing the order of x Vx4 + y? integration. Sketch the region of integration.

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Q: a Va - х dx ? /a - x What is the value of integral Vx + Va

A: We will find out the required value.

Q: Differentiate the fol y = (sin x)(lnx) a)

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Q: rst, select appropriate values for u and dv. | and dv =O dx ow, find du and v. Treat a and n as…

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Q: Complete the integration: Ssin (x)cos (x)dx = sin (2x) sin (2x) + C ? %3D 16 32 Determine the yalue…

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Q: Reverse the order of integration and then evaluate. a. Sx? sin(xy)dxdy а. 'y

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Q: e the integral. dx

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Q: 3 3 У(х'у + 2х — у)dx + x (ху — 2) dy 3D 0 3

A: Firstly we find Integrating factor, then find general solution.

Q: Use integration by parts to find the integral. (Use C for the constant of integration.

A: It is required to solve the integration by parts:

Q: Evaluate | dx approximately, using (a) the trapezodial rule, and (b) Simpson's rule, where the…

A: We need to evaluate ∫01dx1+x2 , here a=0 , b=1 , f(x) = 11+x2 We need to divide the interval in 4…