2 years ago

I need help wit dis it hard plz

1 answer:

8 0

It is the one in the bottom left corner. This is because you start with the number on the right (7) and plot it on the y axis (the vertical line in the middle). Then you take the slope (3x) and view it as 3/1. Start at 7 and go up 3 and then over one. Continue this until you have a line.

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Use the Shell Method to find the volume of the solid obtained by rotating region under the graph of f(x)=x^2+2 for 0≤x≤5 about x

Irina18 [472]

For each x in the interval 0 ≤ x ≤ 5, the shell at that point has

• radius = 5 - x, which is the distance from x to x = 5

• height = x ² + 2

• thickness = dx

and hence contributes a volume of 2π (5 - x) (x ² + 2) dx.

Taking infinitely many of these shells and summing their volumes (i.e. integrating) gives the volume of the region:

$\displaystyle 2\pi \int_0^5 (5-x)(x^2+2)\,\mathrm dx=2\pi\int_0^5 (10-2x+5x^2-x^3)\,\mathrm dx=\boxed{\frac{925\pi}6}$