Evaluate 40y dS where S is the portion of y = 3x +3z2 that lies behind y = 6. S

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A:

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A: We can evaluate the given integral by using the following formula.

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A: Find dy

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A: The integral is given by,

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A: Given y=x37-x6 To find  dy=?

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A:

Q: Vr' +y? ydzdydx x² + y? +z? x²+y² 3 Jo Jo

A: Given:           ∫35∫0x∫0x2+y2ydzdydxx2+y2+z2       ∫0x2+y2yx2+y2+z2dz        =y∫0y2+x21y2+x2+z2dz…

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A: The solution is given below

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A: topic - derivative of a function

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Q: 9.) S(5t + 2t2 - 5t - 50)dt

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Q: 3 | (16t³ – 9t² + 7)dt Evaluate:

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A: We can find y' and y'' as below

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A:

Q: y=(x+5)^x Differentiate

A: Solution: y=(x+5)^x dydx=ddx((x+5)x)

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.