True or False? Var(Y|X) is calculated as ∫(y −μy)^2*p(y|x)dy where μY = E(Y).

Q: 2. xy dx dy

A: While integrating wrt 'x' we will keep 'y' as constant. While integrating wrt 'y' we will keep 'x'…

Q: If the change of variables u=x²+4 is used to evaluate the definite integral f(x) dx, what are the…

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Q: an integrating factor for the DE dy+ydx=e3x dx is  1)ex 2)x2 3)y 4)x 5)ey

A: To find an integrating factor for the DE dy+ydx=e3x dx

Q: Find: 1. integral  ∫cos(lnx)/x2 2. integral ∫x3√1 − 2x dx 3. the average valueof…

A: 1. integral  ∫cos(lnx)/x2 2. integral ∫x3√1 − 2x dx 3. the average valueof f(x)=2−6cos(0.09(x−π)) on…

Q: 4 Given the integral: Jo 1+x² dx. Evaluate using Romberg's method. Tolerance = Nx10-6

A: Given integral, I=∫014 1+x2dx To find: Value of integral using Romberg's method

Q: Reducible to Exact (2xy ln y)dx+(x2+y2√y2+1)dy=0 Have to be convert to exact by integration method

A: Given  Differntial equation (2xy ln y)dx+(x2+y2√y2+1)dy=0

Q: 20. Evaluate dædy by changing the limits of integration appropriately. e y/2

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Q: `s): The area of the surface obtained by rotating the curve y = ln(3x - 2), for 3 ≤ x ≤ e², about…

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Q: 1. Integrating factors found by inspection: (xy + xy)dx+(x²y²-2)dy = 0

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Q: Reducible to Homogenous method dy X-y-3 x-y-1 dx

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Q: 412 Evaluate the integral (x² + y² + z²) dz dy dx. SSS 000 412 SS S (x² + y² + z²) dz dy dx = [ 000…

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Q: 2. Integrate numerically the given function, fx0.1(1.2-x)(1-e20(x-1)) dx with the multiple-segment…

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Q: Solve the DE by Integrating Factors Found by Inspection 3 1. x dy - y dx = x¹ y dy + x³y² dx X

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Q: Using u = 1 + t°, the limits of integration will change from t = 0 to u = and from t = 1 to u =

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Q: Find the most general antiderivative. 9 dx -x2 x zX - IN

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Q: 10. f (x) = x² + 4x + 4 Opens up/down:. Vertex: Axis of symmetry: Solution(s): y-int: Domain: Range:

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Q: 1 The volume of a right circular cone of radius r and height y is given by V = T2*y. Suppose that…

A: use implicit  differenetiation to find the unknown.

Q: [2] Determine the values of n and h required to approximate | a In(x)dx to within 10-10. Use (a)…

A: Hello. Since your question has multiple parts, we will solve first question  for you. If you want…

Q: Reducible to Exact (2xy ln y)dx+(x2+y2√y2+1)dy=0

A: We have: M = (2xy ln y)dx ∂M/∂y = 2x(1 + ln y) N = (x2+y2√y2+1)dy ∂N/∂x = 2x

Q: y(x* – y²)dx + x(x* + y²)dy = 0

A: Let us consider the differential equation,  Where M and N are the function of  x and y. If the…

Q: 7. Evaluate the improper integral. -kx e (k: constant)

A: Please refer to the image below.

Q: 90% of it Suppose dy/dx = x-y and y = 2 when x 1, Use Euler's Method with increments of Ar = -0.1…

A: Given the differential      dydx=x-y with y(1)=2. Find y(0) using Euler's method with step size…

Q: What is the antiderivative of 1 / (x - (1/k)x^2) with respect to x? k is a constant

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Q: From the differential equati on by eliminating the arbitrary function ffrom xyz = f (x?+y'+z°).

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Q: If the change of variables u = x + 1 is used to evaluate the definite integral f(x) dx, what are the…

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Q: 4. Use the Fundamental Theorem to evaluate (x³ - 6x)dx . (Your answer must include the…

A: Use the integral of polynomial.

Q: 2. f(x) = _x- 2 4x + 4 Holes: Vert. Asy: Hor. Asy: x-int: y-int: Domain

A: We can answer all the subparts as below

Q: 1. Integrating factors found by inspection: (xy’ +xy dx +(xʻy² – 2 kdy = 0

A: A differential equation of the form M(x,y)dx+N(x,y)dy=0 is said to be exact iff ∂M∂y=∂N∂x

Q: 2 3 2 Q5. Evaluate the value of integral |[xy'z dx dy dz . 0 11

A: I have stated the used formula in the solution

Q: (b) Use the total differential dz to approximate Az. dz = X

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Q: 3. f(x) = _-x² +1_ %3D 9- x + zX Holes: Vert. Asy: Hor. Asy: x-int: y-int: Domain 4. f(x) = x3 – x2…

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Q: The integrating factor of the given DE are already given below. What is the value of "n"…

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Q: .4 4-y Q3) Evaluate triple integral , S S dz dy dx.

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Q: 1. Find the general antiderivative. A. S 5x8 4x4 + 10x3 – x² – 9x + 15 dx В. /2 - cos x + sec x ·…

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Q: - 3+ In x 3+ In x dy show that dx 2. (i) Given that y = [2] x(3 + In x)? 12 (ii) Hence evaluate dx .…

A: (i) Given : y=-3+ln(x)3+lnx Therefore, taking derivative both sides w.r.t x :…

Q: Find the antiderivative for the given function. 3x tanh(x*) 1) In(cosh(x*)) +C 2) In(cosh(x*)) + C…

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Q: I. Integration by pa 1. Su²sin2u du 2. S y²e2ydy

A: The given integral is,1.∫u2sin2u du2.∫y2e2ydy

Q: The value of the integral 1 2 x²y° dy dx is: 2..3 1

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Q: | by inspection: (3y° + xy kdx + (x°y² – 2}kty = 0 1. Integrating factors found

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Q: Evaluate the Double Integral. 4 V16-x2 b. 2x dy dx

A: We have to evaluate

Q: 5. Given the function f(x) = 1 + ex sin(4x) with integration limits from a = 0 to b = 1. Use…

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Q: 39. Use Leibniz's Rule to find the value of x that maximizes the value of the integral px+3 1(5 – t)…

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Q: 5. Evaluate the definite integral (1+lnx)² dx а. 1 dx. b. -1 2x+3

A: Explanation of the answer is as follows

Q: Find the general antiderivative of f (x) = 4 x ln x²

A: Given: fx=4xlnx2

Q: Use the Romberg integration to evaluate. 3 xe*dr With an exactitude e =0.5%

A: Given ∫03xexdx whose step error should be εs=0.5%. We use the Trapezoidal rule…

Q: Using Simpson's method Vx dx for n=4 is equal to

A: We have to evaluate ∫01xdx for n=4.

Q: Q3) Evaluate triple integral S" dz dy dx. x-y

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Q: B. Integration by Parts 1. xcosx dx

A: We know that integration by part formula is given as  ∫uv dx = u∫vdx - ∫dudx∫vdxdx To evaluate: ∫x…

Q: 1 The volume of a right circular cone of radius x and height y is given by V TXʻY. Suppose that the…

A: Given that:                        Volume of the cone, V=13πx2yV=204π cm3x=6y=17

Q: 4 16–x² Change the order of integration. Do Not Evaluate. 5tan xy dy dx

A: Answer