Question

Could anyone help with this question

Answer 1

k = 96

Explanation:

`f(x) = x\sqrt{(6 -x^(2)) } \\\\ = x(6 - x^(2))^{(1)/(2) }`

`V = \int\limits^2_ {-2}\pi (f(x))^(2) \, dx \\\\ = \pi \int\limits^2_ {-2} (f(x))^(2) \, dx \\\\ = \pi \int\limits^2_ {-2} (x(6 - x^(2))^{(1)/(2) })^(2) \, dx \\\\ = \pi \int\limits^2_ {-2} x^(2)(6 - x^(2)) \, dx \\\\ = \pi \int\limits^2_(-2) 6x^(2) - x^(4) \, dx \\\\ = \pi [(6x^(3) )/(3) -(x^(5))/(5) ]\limits^2_(-2) \\\\ = \pi [(2(2)^(3)-((2)^(5))/(5))-(2(-2)^(3) - ((-2)^(-5))/(5)) ] \\\\ = \pi[(16 - (32)/(5)) - (-16-(-(32)/(5)))] \\\\ = \pi[(48)/(5) - (-(48)/(5))]`

= π[⁴⁸/₅ + ⁴⁸/₅]

= π(⁹⁶/₅)