shynes
shynes shynes
  • 26-04-2021
  • Mathematics
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Please I need this asap, my answer is wrong

Please I need this asap my answer is wrong class=

Respuesta :

nuuk nuuk
  • 01-05-2021

Answer: [tex]512\pi[/tex]

Step-by-step explanation:

Given

Equation of curve is [tex]x=\sqrt{8+y}[/tex]

When this curve is rotated about the y-axis, then volume generated is given by

[tex]V=\int_{a}^{b}\pi x^2dy[/tex]

When [tex]x=0[/tex], [tex]y=-8[/tex]

Put the limits and solve the integral

[tex]\Rightarrow V=\int_{-8}^{24}\pi (8+y)dy\\\\\Rightarrow V=\pi\left ( 8y+\dfrac{y^2}{2}\right )_{-8}^{24}\\\\\Rightarrow V=\pi \left ( 8\times 32+\dfrac{24^2-8^2}{2}\right )\\\\\Rightarrow V=512\pi[/tex]

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