iii) So z dx 1+x2

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A: Given X~Unif(0,2) Result: if X~unif(a,b) then  Mean=(a+b)/2 Variance=(b-a)2/12

Q: 14. Consider that * Sof (x)dx = 2 and f'(1) = 3. Find Soxf"(x)dx. %3D 3 O 5 O 1 O 4 O 2

A: We have to find

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A:

Q: .'( , "ג oa3 (125x*y)" 学 A: 125 2 3 $%% 1/3 5メ Y C: D: VONE OF THESE

A: Since you have asked multiple questions in a single request, we would be answering only the first…

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A: We have to find integral

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A:

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A: ∫1-1∫0x2-1dy dxWe need to evaluate the above double integral.

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A:

Q: 2 Evaluate the integral S (3x³ – 2x² + x) dx. 1

A: We solve it by integrating polynomial

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A:

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A:

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A: We have to find out derivative

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A: Given:-  ∫-11(1-x2) p'l(x)p'm(x)dx=2l(l+1)2l+1δlm

Q: Integraate :S, 22+x+! d>x 2.

A:

Q: X, t Xx t 2 Xz531 2X, + X> t Xz Z22 Naximzed By: 233y,tax2tdxg

A:

Q: -2 -In x SLy e dz dx dy O 7/24 O 7/48 O 5/48 O 47/24

A: We have to find the integral.

Q: S (x+Sy+wz ) dzoly dz 2 3x X-つ

A:

Q: 2) Show that La- (1 – x²)P',(x)P'm(x) dx : 21(1 + 1) Sim. 21 +1

A:

Q: 2こx+iy 2 Recz) =l 3-i1 if 121 =2, then

A:

Q: Evaluate the integral : S 8x2+10x-6 (x-1)(x+1)z dx (2—1)(ӕ+1)? +C

A: Given: ∫8x2+10x-6x-1x+12dx To do: Evaluate the given integral.

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A: The given function z is zx,y=x2y2exy We have to find the partial derivative of z with respect to x.

Q: 2. Determine Var(Y) when Y 3X1 +2X2 with Var(X1) 1, Var(X2) 5, Cov(X, X2) 2, E X1} 3, аnd E{X} 4.

A:

Q: (b) f(z) = tan¯"(5z) - (In(2"))®

A: We have to find derivative

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A:

Q: If k> 0 such that k S x 8k dx = 7 then

A:

Q: 8. Compute using the trig. substitution S x2 -dx (1–x²)1/2

A:

Q: 2. f(x,y) = x5 In(y)

A: Given function is fx,y=x5lny. To find the first and second order partial derivative of the given…

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A:

Q: 23. If exy = 3, then what is Y at the point (1, In3)? dx -In3 3ln3 In3 -4In3

A: Given:- exy = 3 To find:- dy/dx at point (1,ln3)

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A:

Q: :Q3 Classify PDEs below и ди y2 и + и = ue 5x — - ду

A:

Q: (x) = 3x +12x+2, %3D ues of a, b and c such that

A:

Q: In(y) 6° Evaluate dy.

A: Consider  I=∫19ln(y)ydy

Q: 3. Obt nin the parh cular folu tion 9. xdx - ydx + 3x dy +ydy = 0 ; wun x - 5,4= -:

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

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A: we have to find the value of a

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A:

Q: 3. Obtain the 6.S. sy dx + taydy = 0 xcos

A: We have given equation  xcos2y dx+tany dy=0 xcos2y dx=-tany dy x dx=-tanycos2y dy x dx=-sec2y tany…

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A:

Q: 2. § (5z² - 7z + 3) dz from z = 2 to z = 1

A:

Q: Determine the general solution for following Cauchy-Euler Equatio dy + 7x +5y = x³. i) dx2

A:

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A: Using complex contour integration

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A: Using rule of logarithm & integration formula of sech(x)

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A:

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A:

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A:

Q: If [ In(ax)dx = 3, then a %3D 1

A:

Q: 2. Use a theorem to find the ff. Zx if yz? + z = 5xy – 1.

A: Find out the zx when function is given as yz2+z=5xy-1 or yz2+z-5xy+1=0

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A:

Q: 2 Find / U(x) + 4g(x)]dx if -5 2 2 | f(x)dx = 6 and / g(x)dx = -3. -5 -5 2 [f(x) + 4g(x)]dx = i %3|…

A: Given∫-52f(x)dx=6∫-52g(x)dx=-3