Use Green's Theorem to evaluate the integral. Assume that the curve C is oriented counterclockwise. 5x²ydx + 5(y + xy²)dy, where Cis the boundary of the region enclosed by y = x² and x = y². .5x ydx + 5(y + xy°)dy = i

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A: ∫01e12ti + e-t j + t kdt=e12t12i -e-t j + t22 k01=e12112i -e-1 j + 122 k-e12012i -e-0 j + 022…

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A: We can solve as follows

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A: Derivative application

Q: 1. Find the most general antiderivative of the function f(x)D + sin(4- r) +7e

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A: We will use integration by parts and will take values from table to solve this.

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A: h(x,y)=x^3-3x+3xy2 for critical point  ∂h∂x=0∂h∂y=0 ∂h∂x=3(x^2)-3+3y^2∂h∂y=0-0+3x(2y)for critical…

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Q: FOLLOW

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A: To solve the given integral