72 Y : 1 Vt2 +t+1 dt ||

Q: integral of 9(t-1) / t^2(t^2-9) dt

A: Integrate: ∫9(t-1)t2(t2-9) dt

Q: x2y3-y=x+x2 find dy/dt

A:

Q: V49 – t dt t3 Integrate: -C

A: I=∫49-t4t3dt

Q: 7.S dt J VE+2- 5

A:

Q: -1-y 3) Evaluate the integral dxdzdy?

A:

Q: Solve the problem. Suppose that " g(t) dt = 4. Find S* ste) dx and *- gt) dt . -1 1; 4 0; 4 O 1; -4…

A:

Q: 1 x+1 Integrate: r21?

A: Here we have, I=∫01x+1x2+2x2dx

Q: d²x dx 2 + 10x = e2t x(0) = 0, x'(0) = 1 %3D - dt2 dt

A: Given differential equation is d2xdt2−2dxdt+10x=e2t. and x0=0, x'0=1 Write the auxiliary equation…

Q: d?x ax dx ÷+ 9x = 0, when x(0) = 1 and (0) = 0 dt2 dt dt

A:

Q: ex: show that (H.W) (xJ,(x)' = -x Jv+1

A:

Q: --——-^*[e'-In(2t+1)]dt, find g'(x) . dx 4 A e*+ (2x + 1)² 4 B et + (2x + 1)² 2 (C) e*- - (2x + 1)²…

A:

Q: Find the linearization L(x) of y = e In(x) at a = 1. L(x) = %3D

A: Given a function f(x)=y=e3x ln(x) To find the linearization L(x) at a=1 The linearization L(x) is…

Q: 2x For x > 0, In (t +1) dt %3D da A In (2 +1) In (8z + 1) 2 In (2 + 1) 3. 2 In (8z +1) E 24x In (8z…

A: Considering the derivative of the integral

Q: Find the general solution of the DE: dx 6- dt2 + 12- - 8x = 0 %3D - dt3 dt

A: Given ODE is d3xdt3-6d2xdt2+12dxdt-8x=0

Q: Integrate (a) S2(* dt (b) S(x+1)³ dx (c) cos(-x)(x²)dx

A:

Q: Transforming A S B © D dx secx + 1 7 dz 1-2² 1==323d² -dz 1+z² [1+2²21 2-272 1+z² -dz -dz using…

A:

Q: 5. dt3 d³x(t) 8 d²x(t) dx(t) - - dt + x(t) = u(t) 14 dt2 d²x(0) 1, dx(0) x(0) = 1 -2, dt2 dt

A: Given below the detailed solution

Q: 1 dy J yi + 3y² + 1

A:

Q: Using the second fundamental theorem of calculus and chain rule, compute dz t dt. t+1 2x

A:

Q: 10e. Integrate F (1) dt

A: Given that rt→=t+1,t,1t.

Q: Integral of (dt)/(t^2sqrt(t^2-16))

A:

Q: |1-y2 ху Q3. Evaluate the double integral dxdy /1– y²,

A: We have to find solutions

Q: If x, y, and z are lengths of the edges of a rectangularbox, then the common length of the box’s…

A: Given- s=x2+y2+z2 To find- dsdt in terms of dydtand dzdt, if x is constant. Concept Used- As the…

Q: d csinx 1 dt 1-t2 dx '3 V5 SNt VE2 + 1 dt 1+xv

A: We have to solve the integral

Q: 1/4 sec2(t) dt J-x/4

A: Given: I=∫-π4π4sec2tdt

Q: Find the total differential z = 5x3y2

A: The given function is z=5x3y2. Total differential: Let z=f(x,y) be continuous on an open set S. Let…

Q: 4. Prove that: Jx'J,Ex) dx 2 3x J,Cx)-(x-3x) J.cx) -3

A: We find the value of the integration by apply the integration by parts and the recurrence relation.…

Q: 3D In Vi dt y = x/2

A: First of all we will evaluate  ∫lntdt=∫ln(t)12dt=12∫ln(t)dt=12ln(t)∫dt-∫ddx(ln(t))∫1dtdt(used…

Q: = S, (x²(t) + x²(t))dt %3D x(0) = 1, x(1) = free %3D

A:

Q: 10. Integral 2-t dt

A:

Q: s^2ds+2t(s+1)dt=0; s=0, t=1

A:

Q: 4. Compute dx S in two ways and verify that the answers agree.

A:

Q: 10. Using the substitution u 2x - 1, prove that %3D 3 8 dx J1 (2x-1) 25

A:

Q: d²x dx dx -(1) = 2 4- + 4x = 0 x(1) = 0, - dt2 dt

A:

Q: %3D MUTM az əz +y= əz X- dv ay TTM UTN

A:

Q: Solve the IVP 3 d.x dx a(0) = 1, = 2. dt \t=0 dt2 dt

A: Given d2xdt2=-x(dxdt)3, x(0)=1, dxdt|t=0=2

Q: What does Cauchys EU theorem guarantee for The IVP:  dy/dt = -(y)^2/2t,  IC: (to,0)

A: Ft,y=-y22tDomain:{t,y∈R2:t≠0}∂F∂y=-ytDomain:{t,y∈R2:t≠0}∴function Ft,y is continous.So there exists…

Q: dx = x(x 1)(x + 1) dt has a solution that is

A:

Q: By the Fundamental Theorem of Calculus: •t „2 +1 dx 5x +1 d dt d and dt - 6t x2 +1 dx 5x +1 d…

A: Given

Q: 1. Determine the general solution of (x 3y )dx – x dy = U

A:

Q: E valvate cox³ (x²+3)dx 2.

A:

Q: * Lct X; ~ exp (2) · Show that T= EX, is Su fficient pro pesty of T %3D

A: How to find the sufficient statistic 1. Find the likelihood function 2. Apply the Neymann…

Q: d?x dx + 4 + 5x – 10 = 0, when t = 0,x = 0,x = 0 %D | dt2 dt

A:

Q: 4. Prove that ах x" ea" dx xn- п-1 ‚ax dx а а

A:

Q: d²x dx + 4- + 5x – 10 = 0, when t = 0, x = 0,x = 0 dt2 dt

A:

Q: - = 2x, – x, dt dx, =-x, +x, +4e' dt

A: integrating, x1= (x1)^2-dx2/dt, replace dx2/dt with -x1+x2+4e^t in above equation…

Q: d²x + cos(t)- dx sin(t)- + sin(t)x = tan(t) dt dt2 x(1.25) = 6 dx = 5 dt 1.25 has a unique solution…

A: The differential equation  d2ydt2+ptdydt+qty =rt                    .......1 with conditions yt0=y0,…

Q: Show that * Ső› X yn+¹ J₁ (xy) dy=Jn+1 (x)

A: Using the recurrence relation of bessel function

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