2 3 dt. 0 1+t2

Q: 10 (3-t)√t dt

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Q: 1 t² dt 4 0.

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Q: (du/dt)^3 – (du/dt)^2 – 2u = 0

A: Given: (du/dt)^3 – (du/dt)^2 – 2u = 0 Find : solve the differential equation

Q: 2x" + x' + 8x = t+1 t±¹, x(0) = 1, x'(0) = 0.

A: given 2x''+x'+8x=t+12 with conditions x0=1 , x'0=0 solve the equation using method of variation of…

Q: -dt (t+1)ª (t–1)*

A: Solution

Q: (4) t(s² + t²)ds – s(s² – t²)dt = 0

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Q: 13. f(x) = {1 + x, 1, -5 <x <0 0 sx <5

A: Fourier series

Q: Ex: evaluate 1 203 (1- 3 (1 – t)0.9 dt 0.

A: Explanation of the solution is given below...

Q: (1+t^2 )ds+2t[st^2-3〖(1+t^2)〗^2 ]dt=0 when t=0, s=0

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Q: [ -1 + dt X2 with x1(0) = 1 and x2(0) = –1.

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Q: – 2) dt. Then fC

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Q: 2. 2 PCn):芝(-リ 2h %3D j = 1

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Q: Find dy/dx

A: We have to find  dydx where y=∫0xt3+110dt3

Q: t-1 y = t.

A: Given that, x=tt-1y=t2t2-1 Then we get,…

Q: 3. r(t)dt. 1 Part B. Evaluate 10

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Q: 2. x"(t) – 4x'(t) + 4x(t) = 4e²t; x(0) = –1, x'(0) = -4 %3D

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Q: Evaluate (t – 4/i +t-')dt

A: Given : ∫t -4t + t-1dt

Q: 1 9 1 dt 1 + t2 %3D II

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Q: dr 19. 1/2 23 de 21. (2-z 2) dr 22. t 1/2 dt 27 t +1 dt 23.

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Q: 1. Marjinal maliyet Fonksiyonu f'(x) = e=* +: + Vx2 olan bir (1-2x) firmanın maliyet fonksiyonunu…

A: Given marginal cost  f'(x)=e-x+11-2x+x23 To find the cost function    Cost function f(x)=∫f'(x) dx

Q: 2. Solve the following: dt x> 2 X-y t+

A: The formula for the substitution method for definite integrals is given by , where g'(x) and f(x)…

Q: 1. 2tds + s(2 + s²t)dt = 0

A: As per our guideline we are supposed to answer only one asked question.kindly repost other question.…

Q: dt d 24. (u(et- 1)) dt t=0

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Q: d 20. a) dt b) Evaluate: + dt 1

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Q: 0.125 А. f(8t) dt | 0. 0.25 B. f(1 – 4t) dt = 2.5 c. f(5 – 2t) dt =

A: Given that,

Q: 1 2(1-z) 3(1--z) dydxdz = 1 0 0

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Q: 2. (1+t²) ds + 2t[st? – 3(1+t²)²]dt = 0; when t = 0, s = 0

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Q: 10 | (1-e-t/4) dt 0,

A: Given integral, ∫0101-e-t4 dt

Q: 1 1 -dt 4 W (t+1)* (t-1)* 4 (t+1)ª

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Q: (ii) (2 – t4)4 dt *xª – 5x³ + 6x² – 18 dr g3 – 3x² (iii)

A: 2)

Q: Vy = 2 Input Output 1 -2 -0.5 %3D - -1 -1 1 1 Vy = va %3D 2 0.5 3. 0.33 Vy = |a| %3! b. Input Output…

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Q: If 立= 2t, t-3t dt, then |ü||=

A: To find ||u||^2 from the given integral.

Q: 5. /(들+ 4) dt + 4t3 ) dt is -+ t+ + C, b.는+ t® + C,c.는+t+ + C а.

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Q: s 1 s(s+ 1)² -1 +et+2te-t Option 1 2+te-t Option 3 - 1 + e-t2te-t Option 2 -2+te+e-t Option 4

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Q: (2n Yn+2 + ) yn+1 ) Yn = (2n + 5)2" cos (") %3D 2n+3 2n+

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Q: 4. du =u -1 dt du =v -1

A: The system is dudt=u-1 and dvdt=v-1. The vector represented by it is u-1 , v-1 Take I quadrant: At…

Q: 7) t(2w – t + 1)dw + w(3w – 4t + 3)dt = 0, when t(1) =-1

A: Given differential equation  t(2w-t+1)dw+w(3w-4t+3)dt=0  , when  t(1)=-1

Q: 2e-0.8t dt, n = 5

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Q: 2 X u"(x) = −3−2x −²_² +6e² + ½f" (x −1)²u(t)dt, u(0) = 0, u'(0) = 1,u*(0) = 2. - 2

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Q: 4 e 2t8(t + 3)dt 00 | 4e -"6(t + 3)dt =| - 2t "8(t + 3)dt: - 00

A: Definition of delta function  Then spilting the integrals we can get the answer.

Q: 2可 S dt 二2可

A: We can do the problem by doing simple integration and then putting the upper and lower limit.

Q: Solve the Attached differential equations?

A: The given differential equation is t-13dsdt+4t-12s=t+1,  t&gt;1. It is same as dsdt+4t-1s=t+1t-13,…

Q: c. St VE² + 2 dt In: Inx d.

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Q: X+x- L-X+, dt 2 x²-1

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Q: du 103. dt Vř – i' 3 1> 1, v(2) = 0

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Q: 1. 3 (t + 3) est dt =

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Q: (1+t2) ds + 2t[st2 – 3 (1+12) ²]dt = 0; when t = 0, s = 2.

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Q: -4 3 (x²-y²)²] x+y Evaluate: ₁ du dt

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Q: 7. Express as a single traction 1 4 X +1 x - 2 8. Express as a single traction. 2x - 1 + 3x + 1 4 3

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Q: 1 2, 1)dt '1+t calculate

A: