Prove that m-l dx =0 m +n (し+x)" where m,n are both Positive

Q: 10. Prove by using integration by change in variable the ff. integral: dx :du 3D arcsecх+ С xVx2 – 1

A: We have given the integral ∫dxxx2-1 = I(say)     Put   x2-1 = t   ⇒x2= t2+1     Differentiate w.r.t…

Q: In ir le) secx dx to be integrable using the formula What should be the value of A for 2- sec x…

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Q: (2- sec?x) " sec(3А — х) e In (a le) sec3x -dx to be integrable using What should be the value of A…

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Q: dy Use dsolve to solve dt 3D 5у — 5ty³

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Q: Evaluate the integral dx (2x + 11) by making the appropriate substitution: u =

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Q: Use symmetry to evaluate the double integral. Ja+ (1 + x8 sin(y) + y sin(x)) dA, R= [-π, π] x [-π,…

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Q: Evaluate iterated integral.

A: Given, ∫01 ∫36 xx2+3y dx dy

Q: the double integral dy dz Evaluate

A: The given integral is: We can solve this integral by changing the order of integration. Consider…

Q: Evaluate the double integral : dy dz

A:

Q: Using appropriate substitution, the integral *+imx) dx is equal to: an

A: From the given problem:   I=∫141+lnx3xdx...1   Substitute in equation (1).   1+lnx=u...Differentiate…

Q: Use u-substitution to evaluate the integral. 3 + 5 Vx dx 3 2 + 5 Vx dx =O

A: Given query is to eveluate the integral.

Q: Calculate the integral (а) dx (*/3 Vtan 0 (b) п/4 -do sin 20

A: Given : (a)  ∫-∞∞x5e-x2 dx    (b) ∫π4π3tanθsin2θdθ

Q: Evaluate the integrals in Exercises: -1/3 6 dx VI + 9x? 5- TT cos x dx Jo vī + sin²x Vi + sin²x 6-…

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Q: Calculate the integral π∫−πDN(z)dz.

A: Given Data The integral is:  πꭍ-πDN(z)dz.   Compute the integral πꭍ-πDN(z)dz, Here C is constant.…

Q: Evaluate the improper intergal 1 dx using the residue (x2 + 9)* theorem.

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Q: Df be areal value integrable on [0,11 f(x)dx =1. t

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Q: Determine the exact value of the multiple integral -In 101 ex-y+z dx dy dz – In z JIn 99

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Q: Calculate the double integral. 9x sin(k + y) dA, R = 0, 풍핑x [o, 플]

A: First we will evaluate the inner integral wrt 'y' and then evaluate wrt 'x'.

Q: Compute for the value of constant (C) by solving the given DE using integrable combination. Let x=1,…

A: Given xdy-ydx=4x4dx

Q: In?(In(ar)) dr. a >0 -dx, a > 0 а. 2.x In(ax)

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Q: dx%3D 9+x²

A: Solution is given below:

Q: Evaluate the integral.

A:

Q: Calculate the double integral. 7x sin(x + y) da, R = [0, * [0, =]

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Q: Evaluate the double integral: dy dr

A:

Q: Show that+ = 0, %3D ax dy? where f(x, y) = In(x² + y²) + tan¯'(²) %3D

A: The partial derivative of a two variable function fx,y with respect 'x' can be calculated by…

Q: (d) Prove that 1-cos 2x dx is divergent. Hint: Split the expression inside the integral into two…

A: Integral is converges or divergence

Q: Evaluate the integral: + 6 dx = %3D

A: Find the integral by using substitution method

Q: Evaluate the integral ∫(5x -1)2 dx by two methods: first square and integrate, then let u = 5x - 1.

A: To evaluate the integral ∫5x-12dx

Q: (유) 6. dy dr Evaluate the double integral:

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Q: Evaluate triple integral , S S dz dy dx. 4-y -2 Jx2 Jo

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Q: Evaluate the integral. /9-x2 dy dx dz = /9-x2 (x² + y²)!/2 3 J

A: Straightway, without any further delay, please convert to cylindrical coordinates: x = rcost; y =…

Q: Find the length of x = In(sin y) from y = to y = . %3D

A: The arc length of a function is the length of a curve fy on an interval a, b given byL=∫ab1+f 'y2dy…

Q: Evaluate the iterated integral. rIn(x) xe-Y dy dx dz 4z 434 3

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Q: 1+1 dz is 1+ z6 By comparison test, the improper integral

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Q: sketch, reverse and evaluate the integral dy dx

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Q: 4 -dx is divergent. 1-2х (b) Show that the improper integral

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Q: Vx 3+4x+8 dx 2 vã (Vx?)

A: The given function is x34+4x+8xx23 We have to identify u and du and the form of the integral of this…

Q: Estimate the value of the definite integral + 2) dx by using the Trapezoidal Rule. (Round your final…

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Q: Evaluate the integral. e sec²(8x) dx %3D +C

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Q: Evaluate the iterated integral. 3 4ze dy dx dz

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Q: 7. Find the indefinite integral. 1. dx V9-16x? 4x 1 tar arcsin 3 +C_b. arcsin(9x) +C a. 4 4x c.…

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Q: Evaluate the improper intergal 1 dx using the residue (x² + 1)3 theorem.

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Q: Find the value of 'h' in 8 dx evaluating by 1+x Trapezoidal rule braking in 24 intervals. 1.25 0.25

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Q: FCx) is continoos on L3,5) and S Fex) dx= 5 Evaluate integral

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Q: Evaluate the double integral : re dy dx 4

A: Given,          ∫1e∫467xdydx

Q: dx, Evaluate the improper integral : [° 6x³e-3x°

A:

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.