The functions f and g are integrable and J f(x)dx = -2, Į f(x)dx = - 8, and I g(x)dx = 3. Use these to complete parts (a) through (f). .....

Q: Q2/ Prove that 1 dx = v2 Jo 1+sin(x)

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Q: Find the differential and evaluate for the given x and d/x of the function, y = tan x, x = 0, dx =…

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Q: By algebraic substitution, the integral - dx dx is converted to: 4+x 2ydy (A y+4

A: Option a is the correction and other option does not satisfy the given conditions

Q: B- Evaluate the integral 1-x (3-x-y dz dy dx /1-x²

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Q: e ln (a le) – sec²r) sec(3A – x) sec'x What should be the value of A for to be integrable using the…

A: The given integral is (2-sec2x)eln(π/e)sec3x/sec(3A-x).

Q: Evaluate the integral (2x – y) dx + (x + 3y) dy along the path C. C: x-axis from (0, 0) to (0, -3)…

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Q: Suppose the curve y = f(x) passes through the origin and the point (1,1). Find the value of the…

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Q: The integrating factor of the linear DE dy 4y = -9 sinx, dx is the function µ(x) = e. Select one: O…

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Q: Evaluate the integration of the function. f(x) = 1+ e-x sinan over the fixed interval [a,b] = [0.1]…

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Q: d) Evaluate using integration by parts: J(x+ 2)In x dx

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Q: Evaluate the line integral (-3x+y)dx + (x + 3y)dy, where C lies along the x-axis from x = 0 to x = 6

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Q: X' 2 -1 Vx * dx X,

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Q: Evaluate the iterated integral. (x² – y²) dy dx -1J-4

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Q: Find a solution for the DE subject to the indicated initial condition: dy dx + P(x)y= x, y(0) = 1,…

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Q: Find the double integral [[ f (x, y)dA for the function f(x, y)=1-6x²y and R:0<x<2,-1 <x< 1.

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Q: The total differential of the function: z=x*e3y . .A dz = e 3Y dx +3x“dy. .B dz = 3x"e3Y dx +4x°edy.…

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Q: Use the fundamental theorem of calculus and the chain rule to find (A(x)) where dx e2x A(x) = In(t?)…

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Q: Evaluate the iterated integral. V1- x8 dy dx

A: We have to find

Q: Evaluate the iterated integral. /2 x. 4 cos (x + y + z) dz dx dy

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Q: Construct the Green's function for d²y dx² dy + (k?x² – 1)y = 0, + x dx subject to the boundary…

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Q: Evaluate the integral arcsin a dx. 1- a2 x arcsin x + C 4 + C Væ2 – 1 + C V1 - a? O x arcsin a + V1…

A: We will use Substitution and then Integration by parts

Q: Assume x and y are functions of t. Evaluate dy,dt for each of the following.:…

A: We have the given function in x and y as 2xy-5x+3y3=-51 On differentiating both of the side with…

Q: Rewrite the equation such that each resulting term or combination is in an integrable form. e y dx -…

A: The given equation is e-ydx-9xdx=xe-ydy

Q: Evaluate the iterated integral. (x² – y²) dy dx -1J-2

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Q: Evaluate the iterated integral. V1- x4 dy dx

A: The given integration,           ∫01∫0x31-x4 dy dx

Q: Find the differential dy and evaluate dy for the given values of x and d.x y = Vx2 + 24, x = 1, dx =…

A: First differentiate with respect to x then find value at x=1 and dx=-0.1

Q: True or False: For an IVP dy/dx = f(x,y); y(a)=b, if f(x,y) is not continuous near (a,b), then its…

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Q: f(x) = | e 'cos(af(s))ds, 0<x< 1, 0 < a < 1, -SX

A: Given: f(x)=∫01e-sxcosαf(s)ds, 0≤x≤1, 0&lt;α&lt;1

Q: Find the differential and evaluate for the given x and d/x of the function, y = 3x2- x+ 6, x = 2, dx…

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Q: The tangent line to the curve y=f(x) is horizontal at where X = Xo f f(xx) = 00 A O f(xo) = 00 .8 O…

A: The tangent line to the curve y=f(x) is horizontal at where x=x0 if

Q: Using the integration bay parts formula with u = x- dv = cos x dx, the integral x cos x dx becomes

A: The given integral can be solved as follows:

Q: Given y=u^3−u+1 and u=1−x/1+x​, find dy/dx​ at x=0

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Q: The joint PDF of the r.v. A and B is constant on (a, b): a, b > 0n 0.5 0.5|X<0.5).

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Q: The integrating factor of the linear DE dy + ycot x = sin x dr

A: Given: dydx+ycotx=sinx

Q: Find fr and fy. f (x, y) = 4e" dt f(x, y) = f,(x, y) =

A: A detailed solution is given below.

Q: 1š + z² + 2 f(z) = Calcule S f(x) dz.

A: Given data: The expression for the given function is f(x)=(x5+x2+2)/(x3-x). The integral of the…

Q: Evaluate the integral. V16-a? 1 dy dx dz = -V16-x2 (x2 + y?)1/2 -4.

A: We can solve as follows

Q: Evaluate the integral. /9-x2 dy dx dz = /9-x2 (x² + y²)!/2 3 J

A: Straightway, without any further delay, please convert to cylindrical coordinates: x = rcost; y =…

Q: Given that f(x) has second derivative, f(0) = 0, f'(0) = 1, and the line integral | [xy(x + y) –…

A: Compare the given integrand  with Pdx + Qdy P = xy(x + y) - f(x) Q = f'(x) + x2y

Q: Assume x and y are functions of t. Evaluate dy / dt for the following. y3 = 2x 4 + 6 ;        dx /…

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Q: Which of the following is always true for integrable functions f and g? ® S dx =- f(x) g(x) (B where…

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Q: Use the specified substitution to find or evaluate the integral. (Use C for the constant of…

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Q: Find the total differential. z = x sin xy

A: Given: z=x sinxy To determine: The total differential of the given function.

Q: Assume that x and y are both differentiable functions of t and find the required values of dy/dt and…

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Q: assume x and y are functions of t.  Evaluate dy/dt for the following: y3=2x4+6; dx/dt=2, x=1, y=2

A: The given function is  y3 = 2x4 + 6    ...... (1) dx/dt = 2, x = 1,   y = 2

Q: Find the total differential. z = e4x sin(3y) dz =

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Q: Find the differential of the function, y = v1+x O 1) dy = Vx+1 O 2) dy = 2vx +1 O 3) dy = %3D 1 O 4)…

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Q: dx dy. Evaluate by changing the order 4y

A: In the given question we have to evaluate the integration                ∫01∫4yyex2dxdy by the…

Q: The function f(z)=e² is: „(x.y) =e*sin(y) O contiuous in CO u(x.y) =e*cos(y) O discontiuous in CO

A: Use the property of complex function to break in real and imaginary part. Here also use the concept…