Use the an approach of cylindrical shells to find the volume created by rotating the an ar bounded by the given curves around the $y$-axis.

You are watching: Use the method of cylindrical shells to find the volume generated by rotating the region bounded by

$$y = e^-x^2,\ y = 0,\ x = 0,\ x = 1$$

How the fudge to be I an alleged to do this there is no parts? Is there claimed to it is in some type of antiderivative come this duty with an $x$ in front of the or something? This is choose three attributes in one.

Obviously i can obtain as far as $2\pi\displaystyle\int_0^1xe^-x^2dx$ however yeah...


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It looks as if you may have reached the appropriate integral, i beg your pardon is$$\int_0^1 2\pi xe^-x^2\, dx.$$You can quickly incorporate by do the substitution $u=x^2$.


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usage the technique of cylindrical shells to discover the volume that the solid derived by rotating the region bounded by the offered curves around the x-axis.
use the method of cylindrical shells to discover the volume generated by rotating the region bounded through the given curves about the mentioned axis.
making use of the an approach of cylindrical shells to discover the volume created by rotating a region with respect to a details axis.
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