Find the function "y" that makes the integral stationary V1+y²y2

Q: Find the derative of the integral from x to 2. y=(t+3)^2 dt

A: let us assume y=∫x2(t+3)2dt

Q: S,(4y³ +-) dy y3.

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Q: Evaluate the line integral along the path C given by x = 2t, y = 4t, where 0 <ts 1. (y - x) dx +…

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Q: Find a formula for the integral. dy = y 3(1– 6y) Incorrect

A: We have ∫e6xe3ydy

Q: Evaluate the integral. dy y+2y-3

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Q: Evaluate the integral. (y – 2)(2y + 1) dy Jo |

A: ∫xndx=xn+1n+1+C ∫1dx=x+c

Q: calculate the integral -2x+4 I=S (x2+1)(x-1)² -dx

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Q: The integral. 1 dydx is VÆ V10 – y3

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Q: Evaluate the double integral : (x + 2y – 4) dy dr

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Q: Find the line integral of ƒ(x, y) = yex2 along the curve r(t) = 4t i - 3t j, -1 <_ t <_ 2.

A: Given: f(x,y)=yex2 r(t)=4ti-3tj -1≤t≤2 From r(t)=4ti-3tj x=4t,y=-3t Differentiate with respect to…

Q: Evaluate the line integral along the path C given by x = 2t, y = 4t, where 0 ≤ t ≤ 1. [ (v - x) dx +…

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Q: Calculate the integral 0∫1xf′′(x)dx if f(0)=7, f(1)=2 and f′(1)=5, where f is a twice differentiable…

A: we have to find the following definite integral. For this we can use integration by parts

Q: Find the integral of ³y²-y+1 f dy y³-y²

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Q: Evaluate the line integral along the path C given by x = 2t, y = 8t, where 0 ≤ t ≤ 1. [(x + 3y²) dy

A: We can solve this as follows:

Q: Evaluate the line integral along the path C given by x = 6t, y = 24t, where 0 tS 1. (x+3y²) dy Need…

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Q: Find the moment of inertia about the​ x-axis of a thin plate bounded by the parabola x=2y-3y2 and…

A: Given that the equation of the parabola,x = 2y – 3y2and the equation of linex + 7y = 0

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

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Q: Find the integrating factor: y(x+y+1)dx+x(x+3y+2)dy=0

A: To find the integrating factor of the given differential equation.

Q: Find the derative of the integral from 0 to x+2 y=(t+3)^2 dt

A: let us I=∫0x+2(t+3)2dt

Q: Evaluate the integral. (Use C for the constant of integration.) t3 In(t) dt C must be in capital…

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Q: Find the line integral of F along the parabola y = x² from the origin to (4, 16).

A: Using green's theorem.

Q: Find y(x) that minimized the integral | using the end conditions y(0) = 0 y'(1) = 0 %3D

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Q: Evaluate the line integral along the curve C. [(x+3y)dx + (x-y)dy, C: x= 2cost, y = 4sint, 0≤ts-…

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Q: Evaluate the line integral along the path C given by x = 2t, y = 4t, where 0 ≤ t ≤ 1. [(x + 3x²) dy

A: To evaluate: ∫C(x+3y2)dy...(1) where C is given by x=2t, y=4t⇒dy=4dt and 0≤t≤1

Q: dt Explain what is wrong with the following integral: |t| VE2 – 1

A: given  I=∫-111tt2-1dt from I  ft=1tt2-1domain of f(t) is t&gt;1,t2-1&gt;0therefore-1&lt;t&lt;1

Q: raluate the double integral : (x + 2y – 2) dy da

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Q: Evaluate the line integral |-ydx + xdy along the curve C : y² = 24x from (24, 24) to (0, 0).

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Q: Evaluate the double integral. y dy dx

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Q: Evaluate the line integral along the path C given by x = 2t, y = 6t, where 0 s ts 1. (y – x) dx +…

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Q: Evaluate the line integral along the path C given by x = 2t, y = 6t, where 0 ≤ t ≤ 1. [(x + 3y²) dy

A: We will calculate the given line integral utilizing given information.

Q: Solve the problem using convolution integral   y′′ + 2y′ + 2y = f(t), y(0) = 0, y′(0) = 0

A: Convolution Integral: Let f(t) and g(t) be defined in [0,∞). Then, the convolution of f(t) and g(t),…

Q: Evaluate the integral.

A: To evaluate the integral: ∫yy+42y-1dy. Using partial fraction decomposition.…

Q: Find the c that satisfies the MVT for Integrals. f(x) = x² [0,4]. over

A: Given: f(x)=x2,  [0,4]

Q: Solve the integral equation, (y(t)), y(x) = 2 + -dt t

A: Given that: y(x)=2+∫1xy(t)tdt

Q: Evaluate the integral; 11 dy dx 1+ 3y3 0 vx

A: Change the order of integration

Q: Evaluate the integral. V3 9earctan(y) dy 1 + y2

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Q: S f(x.y)dxdy- Reverse the order of integration in 0,

A: The given integral is: To find the reverse order of integration.

Q: Evaluate the integral 1. ( (y - 1)(2y + 1) dy

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Q: Evaluate the line integral along the curve C. |(x+3y)dx+(x- y)dy, C: x= 2cost, y = 4sint, 0sts 4…

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Q: Find the iterated integral 1∫0y2∫y(x+2y)dxdy.

A: We have given a double integral;

Q: find the line integral for f = 2x + 2z along the curve x = t2 . y = 3t .z = 2t? where 0<t<1.

A: The objective is to find the line integral for f=2x+2z along the curve x=t2, y=3t, z=2t2 where 0≤t≤1…

Q: Supply the missing integrand and limits of integration. 5 a) S S,2 6x²y dxdy = dy -5 сx/2 b) S S²…

A: We have to find the missing integrand and limits of given integration.

Q: Evaluate the line integral along the path C given by x = 2t, y = 4t, where 0 <ts 1. Lv - x) dx +…

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Q: Evaluate the integral. inegral 1  to 2 [(4 y2 -7y -12 )/ y (y+2)(y-3) ]dy

A: Given:                  ∫124y2-7y-12y(y+2)(y-3)dy   To determine:                    We can solve…

Q: Evaluate the integral. inegral y / (y+4 ) (2y-1) dy

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Q: V.r dx.

A: The given indefinite integral is: ∫xx-x23dx

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: Evaluate the line integral along the path C given by x = 2t, y = 6t, where 0 ≤ t ≤ 1. √(x + 3y²) dy

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