Q2/ A/ Find the and ar * iff (x.y) = x - xy, x=r² +s and y =r-s as

Q: Evaluate the integral dx 2x x - 3x? 1 V3 + V2 x u- - V7 VX + C 2/3 TV3 1 In 2/3"/7x + V3 +C -In 4…

A:

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

A:

Q: Compute.  integral (ex) / (1+e2x) dx.

A: Solving an indefinite integral using a substitution. If we have some function defined as:…

Q: 2. Evaluate the integral 4 dx V2x-5 5/2

A:

Q: 1. What should be A for the path independent of (2,4) xy + A 2dy – x y? fip- (1,2) Moreover evaluate…

A:

Q: Evaluate the integral. /x² – 36 Vx2 – 36 -dx + 6cos + C Vx² – 36 -dx = Vx² – 36 – 6cos- () + C x² –…

A:

Q: 1. What should be A for the path independent of (2,4) xy+ ^ dr + 2Ay – x dx + y? fip- (1,2) Moreover…

A:

Q: Find 1-a Conf int for y txo P( - tor;ou L T L tarziv) =1-a

A:

Q: 2メーx2 Compute the integration dydx (x²,

A: Given:          ∫12∫02x-x21x2+y22dydx       Converting into polar coordinate  It looks like half a…

Q: Illustrate the setting up limits of a double integral?

A:

Q: 1) y = 2sin (5x) ,2) y = In x'n cosh 5x ,3) xsin=14y = y tan-14x 4) y = ecosh (8x),5) y =- t +1 t…

A: As per our guidelines, we are supposed to answer only one question. Kindly repost other question as…

Q: 3/ Find Valke of integral Sx dx

A: Value of the integration

Q: 5. Evaluate the indefinite integral. S cososin'oc (1) (3x - 2)20 dr (2) (3) S etanr sec?rdr

A:

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

A:

Q: 4. Show that evx dx = 2Vxevx - 2ev + C Hint: Make a substitution first before doing integration by…

A:

Q: Queston} $²3 20c x²-4 Composite Trapezoidal rule with n=4 dx. 3.1.1. use the to approximate…

A:

Q: 7. ydx-xdy + xydy = 0 Ans: In²+ y = c

A: We have to solve differential equations

Q: dx 3) L. Vx+1

A: Given:

Q: 8 2 1. Reverse order, then integrate Sr) dydx.

A: Given:    Intergral is given

Q: 2 Find つえdy 2 こ( beny s)

A:

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

A:

Q: 6 Strange fact: 8(2x) is different from 5(x). Integrate them oth from 1 to 1.

A:

Q: Queston 3.1.1. use the 2xc to approximete dx. Composite Trapezoidal rule with n=4 integral. 3.1.2.…

A: Let us consider y=2xx2-4. We have to compute the approximation of the integral ∫abfxdx, where a=3…

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

A:

Q: Evaluate the integral. Sex. cos 3x dx e2x [ sin 3x + cos 3x] + C O e2x [3 sin 3x + 2 cos 3x] + C 13…

A: Given: ∫e2xcos3x dxe

Q: Compute y = S V1 -x dx using Monte Carlo Method. The integral is approximately 1.5708

A: Given that y=∫-111-x2dx By using the monte carlo method, Take x=sinu→u=sin-1x, dx=cosudu Then the…

Q: Use an integrating factor to solve the IVP y'+ytan x = cos x, with IC (x, , Yo) = (0,7), %3D and…

A:

Q: d Evaluate dz 1 dt. 1+ Int

A:

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: 3 Only one of these calculations is correct to evaluate the definite integral Vx²+1 dx -1 Using the…

A:

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

A: Make the given Differential equation in exact form and than integrate.

Q: If the function f(x) is defined on the 2 intervallo, TT) and f'(x) = -cos X (sinx) than f(x) has…

A: Given that fx is a function defined on an interval 0,π whose derivative f'x=-cosx1+sinx2 To find the…

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

A: We will find out the required solution.

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

A:

Q: Create a second order DE (no need for IC's) whose sdution conuergio to O ao t+ o, without…

A:

Q: Put that: coshx- hel x+Jx=I/,.- cosh x= lml x+J xI/ メン」

A:

Q: The integral of the given function csc °x dx is equal to 3cos x-10stn²x cos>x-15sin"xcosx + C…

A: I=∫ csc6x dx =∫ (cot2x+1)2 csc2x dxu=cot xdu=-csc2x dx=∫ -(u2+1)2 du      =∫(-u4-2u2-1) du…

Q: 4d.x To integrate the first step is to decompose the integrand to

A: Integrand is decomposed into fraction.

Q: Find the Integration of: Ja (3sint + esin t) cost dt In 3 2

A:

Q: use integration by parts to establish the reductionformula.

A: To prove, ∫xnx+1dx=2xn2n+3x+132-2n2n+3∫xn-1x+1dx

Q: Evaluate the integral: sinh 3x csch 3x dx coth 3x "+C 3 coth X +C 3 - coth x +C - 3 - coth 3x +C 3

A:

Q: Let f(x) = 1/[π(1 + x2)], −∞< x < ∞ be the pdf of the Cauchy random variable X. Show that E (X) does…

A: Improper integral

Q: NN² 4xy² dydx /4-x2

A: In the given question we have to draw the region of the integration s.t…

Q: Give necessary and sufficient conditions for p(x)/q(x) to be an immediate integral (do not use the…

A: We want a function of the form

Q: Find the integration inner product on C[-3,3] of the given functions. f(x) = 16x g(x) = 3x² (f, g)…

A: Explanation of the answer is as follows

Q: 1. What should be A for the path independent of (2,4) xy + A dx + 2Ay – x y? fip- (1,2) Moreover…

A:

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

A:

Q: Calculate I dx n=LobysimPsons4) rule

A:

Q: Show complete solution Expand, that is, perform the indicated operations on the differential…

A: To expand, that is, to perform the indicated operations on the differential operator, xDD+x