3- Using Beta function, show that dx = Tt (b – x) (x – a)

Q: d Using the Chain Rule Twice Calculate 1+ Vx2 + 1. dx

A: Given function is 1+x2+1

Q: Find the differential dy for the given values of x and Δ x. y = 5x 2 - 2x + 3 ;  x = 2 , Δ x = - 1…

A: Given that: y=5x2-2x+3,  x=2  ,  Δx=-16

Q: e*(1-cos(x)) Exercise: Evaluate S dx.

A: Now evaluate the integral, ∫0∞ex(1-cos(x))xdx Take the minus as outside and it is concluded as…

Q: Find dy for all of : dx 1- y = x/Inx у

A:

Q: Q.2 Evaluate I = f* x*(1 - √x) dx using Beta-Gamma functions.

A: Given: Integral I = ∫01x4(1-x)5dx We have to evaluate the given integral using Beta Gamma function.

Q: Determine whether the equilibrium at x = 0 is stable, unstable, or semi-stable. dx 4x² - x³ dt 3 The…

A: We need to find the equilibrium at x=0 is stable, unstable, or semi stable. given,…

Q: dly dx2 - 2 dy dx -3y = COS X

A: The given differential equation is d2ydx2-2dydx-3y=cosx. We have to find the solution of the given…

Q: dy 1- Find by implicit differentiation. dx 2- x2 + y2 = 100. 3- x3 + y3 = 3xy². 4- x²y + 3xy3 – x =…

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Q: 18 dx Integrate using trig. Substitution: S- x² V9– x²

A:

Q: dy of the implicit function. dx 4. Find the 1 1 1 2 2 = a

A:

Q: d²x dx + 2 * + 5x = e-t sin t; dt [ = x(0) = 0 x'(0) = 1 %3D dt2

A:

Q: Find the differential dy of the given function. (Use "dx" for dx.) y = In (√9-x²) dy =

A: Given: y=ln9-x2 To find the differential dy

Q: Determine whether the equilibrium at x = 0 is stable, unstable, or semi-stable. dx = 3x7 dt The…

A:

Q: Find the differential dy of the given function. (Use "dx" for dx.) y = xV9 - x² = Ap

A:

Q: 1. Find the differential of w = x cos y – y sin x.

A:

Q: dw of w -+ dt X y H.W: Use the chain rule to find the derivative dw with x= cos 1, y = sin? t, z =-…

A: We differentiate the function with respect to t.

Q: £シノ/2 t. dt. 2

A: Given,  12∫0α e-t t32 dt I=12∫0α e-t t32 dt  Let      u=t⇒dudt=12t⇒dt=2tdu Also use, t2=u4 and  t=u2…

Q: What is / - z dx? 1-x² o f- dx = -2cos-lx + C V1-x2 S- dx = 2sin-lx + C (1–x2 S-d 2 dx = 2cos-x + C…

A: 1. I=∫-21-x2dx =-2∫11-x2dx =-2sin-1x+C    ∵As ddx(sin-1x+C)=11-x2⇒∫11-x2dx=sin-1x+C=-cos-1x+C…

Q: (b) by using gamma function x-1/3e-Bx dx

A: Gamma function

Q: Use the information to find and compare y and dy.                                Function    y = 4x3…

A:

Q: by using beta function Vxe-x dx

A: We have to evaluate integral value by using beta function.  I have explained in details please check…

Q: Evaluate in terms of beta function: L (1– 1) dz dr. O-)

A: According to question given:∫01(1-1x)13dxWe have to evaluate the given integral in terms of beta…

Q: x +1 -dx x² (x – 1) (a) Integrate

A:

Q: V3x d. Evaluate dx sin(3t) dt

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Q: -2.1 1- e* Use Simpson's rule to approximate -dx. x² + 2x – 1 1.2

A: This is a problem of numerical Integration.

Q: Let y = tan x. (a) Find the differential dy. (b) Evaluate dy and Δy if x = π/3 and dx = -0.2…

A: Let,  y=fanxa To find differential dy, differentiate y       with respect to x,        dy=sec2x dx

Q: dz Find dz -3 and of z = x³ In(1 + xy). dy

A:

Q: 5 一=A+hxsl-x dy=?

A:

Q: dx1 2.x1 + x2 + x3 + sin(t) dt dx2 = -x2 – 2x3 – 2 cos(t) dt dx3 2.x2 + 3x3 dt

A: According to the given information, it is required to find the general solution.

Q: cos(x² + y²) = y² sinx² y² = ln(x² + y²)

A:

Q: Find the differential of the given function y = xcosx

A: To differentiate

Q: Q1: Find the Integration using Gamma Function Method: x*e-3xdx 0.

A:

Q: 3) Find dy given 3xy = In x. dx

A: Given  3xy=lnx To find dydx   implicit differentiation is used Both sides have to be differentiated…

Q: Find complementary function and particular integral of d²y - y = xe* + cos² x dx2

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Q: ution of yl = x+xy2 W

A:

Q: Find the differential dy of the given function. y = x cos 2x dy Submit Anguer X

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Q: Find the differential dy of the given function. (Use "dx" for dx.) x + 1 4x - 7 dy

A:

Q: Let y=3x^2  Find the change in y, Δy when x=5 and Δx=0.1    Find the differential dy when x=5 and…

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Q: Find oy for dx2

A:

Q: Find the differential dy of the given function. (Use "dx" for dx.) y = (x+2)/(3x-8

A:

Q: Beta Function x dx 3/3 dy (h) 1+ 142/2 that (a)

A: In the given question, the concept of the Beta function is applied. Beta Function is expressed as-…

Q: Find the differential dy of the given function. (Use "dx" for dx.) y = 2√x + +√x dy = Need Help?…

A:

Q: 1. Use residues to evaluate 1 : xe dx , (a>0).

A: Let fz=ze-zz2+a2 The poles of the function fz are ±ai Choose the contour C consisting of the real…

Q: Find the dy/dx of te function using DIFFERENTIATION OF CHAIN RULE, INVERSE AND PARAMETRIC FUNCTIONS…

A: We have - U = x2+113                    ...................(1)Differentiating on both sides with…

Q: 3. Find dy, where; (x+y) = 2 a) cos (xy)- + e b) e+ iPtany=1 , u= xlax (use chain rule)

A:

Q: 1 B3. Evaluate dx, using substitution method.

A:

Q: the differential dy of the given function. (Use "dx" for dx.) y = x(1 − cos(x))

A: Given equation is y=x1-cosx.

Q: a) Find the differential dy of y=x2+2x+5. (b) Evaluate dy for x=3, dx=1/2. (a) dy=????????? dx (b)…

A: GIVEN THAT y=x2+2x+5

Q: dy 1- Find by implicit differentiation. 2- x2 + y2 = 100. 3- x³ + y³ = 3xy². 4- x²y + 3xy³ – x = 3.…

A:

Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.