Evaluate the integral f, (5x + 6y²) dA, where R = {(x,y)|0 < x < 4,0 < y < 3}.

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Q: Suppose an object moves in space with the position functionr(t) = ⟨x(t), y(t), z(t)⟩ . Write the…

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Q: Use a substitution to reduce the ODE to a separable type and then solve it: dy x+y dx x-y

A: To solve the given ordinary differential equation (ODE) dydx=x+yx−y, it can use a substitution to…

Q: for fx xy fy yx f(x,y)=3x³y² + 4(3x + 2y)³ find

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Q: Evaluate the integral f 2x (x² + 6)° dx using the substitution u = x2 + 6. | 20(x² + 6)* dzx +C

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Q: Without evaluating the integral, show that √ √ 2 ² 4+1 4₂ | 15 | 1/2 dz where C is the line segment…

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Q: Calculate the line integral F. dr, where F (3y, -3z, 2x + 2) and C' is the boundary of a triangle…

A: We will find line integral by using stokes theorem .

Q: Find the Cauchy principal value Lant dx (x+1)(x²+2) -R of the following integral R

A: We have to find the Cauchy principal value of given integral.

Q: Evaluate: ²₁¹ (x² - y²) ²1 x+y du du dt

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Q: Evaluate the integral (xy + xy²) dx + (2x² + x²y) dy over the curve C, defined by going in a…

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Q: Arcsin z dz

A: Topic = Integration  As per guidelines, At a time only one question can be answered out of different…

Q: dx 8. Evaluate the integral: J x2 Vx2-16 Vx²+16 a. +C 16x Vx2-16 b. 8x Vx2 -16 ++ C. 16x 1 d. –Vx2 –…

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Q: Let F(x , y , z) = g(y) + h(z) + 5 In(x - 2) , where g(y) and h(z) are differentiable functions of…

A: If a function is a function of more than one independent variable then the derivative of this…

Q: Let f(x, y, z)= exy sin(x+y) Calculate fxxz· z²+1

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Q: /1 x² dx /2 2 x2

A: I am going to calculate this integral using trigonometric substitution.

Q: 16 Evaluate the integral f 2x (x2 + 7)º dx using the substitution u = x? + 7. %3D | 20 (2* + 7)" dz…

A: We need to evaluate the integral ∫2x(x2+7)16dx with the help of substitution. This can be evaluated…

Q: || x dA, R is bounded by y = x, 2x + y = 6 and the y-axis. R

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Q: Consider the function f (x) = cos (2x) a) Find the polynomial of degree 4 centered at X = 1.…

A: The given function is fx=cos2x

Q: s (2i + 2a - 2) dz 4. 1 x3 + 2x3

A: topic - integration

Q: Use two -point gaussian square to approximate the following double integral:

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Q: Evaluate the integral dx (2x + 4)* by making the appropriate substitution: u = dx (2x + 4)°

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Q: Evaluate the line integral of F = [-2.2³ – 2 ·x, −2 · z² + y² — 2, y³ + x] along the z-axis from z =…

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