-) For the function f(t) = 16t3 - 40t consider the definite | integral "f(t)dt -1 a) Evaluate this integral; b) Find all values of x for which the integral becomes zero. Justify your answer.

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A: Given, The differential equation x3+xy2y'=y3 We have to solve the differential equation.  

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A: y = f(x)dydx = f'(x)dy = f'(x) dxy=15+x2dydx = ddx(15+x2)dydx = 1215+x2 ddx(15+x2) dydx = 2x215+x2dy...

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Q: Pro Perties: 1-J-n(x)=-1) Julx)→wisinteger ex Ja(X) J-z(X)=(=1) JalX) - Sてと) ex ゴろしてことづる 2) =c Jelx)...

A: In this question we have to find the equation.

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A: We put y=vx and solve the given differential equation.

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A: Given,Sn = 6 + 0.6 + 0.06 + 0.006 + 0.0006 + ..... = 6.66666...    110 Sn = 66.66666....            ...

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A: Multiply 

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A: topic - slope of the curve

Q: 8. Find when x = t3 -t and y = 4 –- t². dx'

A: Here, the given functions are: x=t3-t & y=4-t2⇒x'(t)=ddt(t3-t)=ddt(t3)-ddt(t)=3t2-1    y'(t)=ddt...

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A: Let's find. 

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A: We know  Sin^2x= (1-cos2x)/2  

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A: Please reupload other parts According to bartleby guidelines

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A: A detailed solution is given below

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A: Giv:    x2 + y2 = ( 3x2 + 2y2 x )2     Point: ( 0 , 1/2 )

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Q: Can you please answer both

A: see below the answer and calculation

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