Find the degree homogeniety of y'=2xy/y^2-x^2

Q: A cylindrical shell has a thickness of 0.2 cm. Using differentials, approximate the volume of the…

A: The volume of the cylindrical shell is given by V=2πrh∆r, where ∆r is the thickness of the shell.…

Q: integral (In x) 3  dx

A:

Q: integral by part x² dx

A: Given that  The integral is

Q: Evaluate ∫x3 √(1 - x2) dx using integration by parts.

A: Consider the given integral Here the objective is to evaluate given indefinite integral.

Q: Evaluate ſe* -3x cos 3x dx using integration by parts method.

A:

Q: tan- Find -dx using integration by parts. x2

A: The given integral is: I=∫tan-1xx2 dx

Q: find derivatines of the first derivatives indol and Zuotients.. y= tanx %3D

A: Given function is y=extan−1x Use formula ddxex=ex and ddxtan−1x=11+x2 Differentiate y=extan−1x with…

Q: Find the exact error in approximating ln(sec(−0.4))by its fourth degree Taylor polynomial at ?=0.

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Q: 8 Evelluate the double integral: + 3x) dydx

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Q: CSCX-1

A: Multiply numerator and denominator by (cscx-1)

Q: 1 find the total differential dz. axeta TU

A: Find dz

Q: Find integration from 0 to π/4  √(secx) tanx dx

A:

Q: 10 Describe a first step in integrating /2 dx. - 4x + 5

A: Given: ∫10x2-4x+5dx Step 1: Taking the constant term outside

Q: Evaluate the integrals ∫(sec2 x) etan x dx

A: Evaluate: ∫sec2xetanxdx

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

A: use substitution method for solving the  integral

Q: Find the indefinite integral using the Chain Rule/U-substitution. 6x dx x2+5 3. 4. S 7xv3x² + 8 dx

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Q: calculate the integral.

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Q: integral of sec^3 x

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Q: he integra = 3/2 is dz Z-2

A:

Q: 2. se integration by pacts to eval integralig x² In (3x)dx niz

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Q: Differentiate: y = ln cosh (cos 2x) 3. O y = 6 sin 2x tanh(cos 2x) %3D O y = 6 sin 2x coth(cos 2x)…

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Q: integral from -1 to 1 of arccos (y) dy

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Q: 4 Use Gaussian Integration (4-point form) to approximate x2sin(x)dx

A: Using 4-point formula the given integration is solved.

Q: Find the area of a triangle bounded by lines y=2x and x=1 by double integration

A: Given region, y=2x        ...(1)x = 1        ...(2) Substitute the value of x = 1 in (1), y = 2 So…

Q: Integral of 2cos^2x+3sin^2x dx from 0 to pi/2

A:

Q: Use the methods of differentials to estimate the value of (x+1) over the square root of 2x+1 at…

A: Use the quotient rule to find the derivative for f(x).

Q: Determine the value of the integral: integral sign:  (x^2)(e^-x^3)

A:

Q: Integral of cos4x dx

A: =∫(cos2x)2dx =∫(1+cos2x2)2dx=∫1+cos2x4dx=∫1+cos22x+2cos2x4dx= 14∫1+cos22x+2cos2xdx=…

Q: 4. Use Trigonometric substitution method to evaluate the integral: dx

A:

Q: Integral of cos2x on [0, infinity]

A: We have to use limits to find the given integral.

Q: Use complex integration to compute 1– cos X dx. x2

A: The objective is to integrate the function ∫0∞1-cosxx2dx

Q: Find the area under the loop of the curve y2=x4(x+4) using integration

A: An integration formula for calculating the area under the curve will be used. We will calculate the…

Q: 6. Carefully interchange the order of integration to evaluate os(x/²) dx dy. COS -1

A: To evaluate: ∫-11∫y21cos(x3/2)dxdy by changing order of integration.

Q: 64 ans: su 3 6. Calculate the area between the Curve fcx) = x²³²_4 and the lines y=2x + 4 and y=0,…

A: area between curve

Q: Find the area of a triangle bounded by lines y=2x and x=1 by single integration

A: A definite integral can be used to compute area bounded by curves. If there are two curves f,g over…

Q: Evalute Sofy ex* dxdy by first reversing the order ex² 3y integration.

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Q: 4. Find derivatice y 4=In (x 3-4x²+1)

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Q: What are the new limits of integration if apply the substitution u = 4x + t to the integral / sin…

A: We have to change the limit.

Q: show that the differential forms in the integrals are exact. Then evaluate the integrals.

A: Here, we have   Assume ∫(0,0,0)(2,3,-6)2xdx+2ydy+2zdz                   (i)   Using the formula,…

Q: Compute the indefinite integral 2. - 4e²² + 6z – 5) 5) dx.

A: We know that integration of ex is ex . And integration of 1/x is lnx. Integration of xn is xn+1/…

Q: cosx dx sin²x-5sinx-6

A: Find your answer below

Q: Integral of sec^4(3x) dx

A: Given ∫sec4(3x)dx

Q: 5. Integrate using an appropriate integration technique. a) ⌠ex sin(ex) dx b) ⌠sin3(2x) cos3(2x) dx

A: use substitution method for finding  integral

Q: COSX - dx sin²x-5sinx-6

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

Q: 6) csch-1x = In Vx2+1 (+ sinh-11 %3D |x|

A: 6. First  we will find relation between csch-1x and sinh-11x. From Hyperbolic trigonometric…

Q: integral In(2x +1) dx

A: Given To Evaluate ∫ln(2x+1)dx