Integration Question (1 Viewer)

Resource · Feb 14, 2015

Hi could someone please help with these questions:

1. if a curve has dy/dx = x/sqrt(x+1) and yint of 2, evaluate y when x=3

2. Find the volume of the solid of revolution formed when the curve y=x(x^3 -3)^2 is rotated about the x=axis from x=0 to x=1

Thanks

FrankXie · Feb 14, 2015

Hint:
$$ 1. $ y^\prime=\frac{x}{x+1}=\frac{(x+1)-1}{\sqrt{x+1}}=\frac{x+1}{\sqrt{x+1}}-\frac{1}{\sqrt{x+1}}=(x+1)^{\frac12}-(x+1)^{-\frac12}$
$$ 2. $ V=\pi\int_0^1y^2dx$

Integration Question (1 Viewer)

Resource

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