find-the-volume-solid-formed-by-rotating-the-area-trapped-between-the-line-y-1-and-the-function-f-x-4-3x-2-aroud-the-line-y-1-

Question Number 90443 by jagoll last updated on 23/Apr/20

find the volume solid formed

by rotating the area trapped

between the line y = 1 and

the function f (x) = 4 - {3 x}^{2}

aroud the line y = 1

Commented by john santu last updated on 23/Apr/20

t h e i n t e r s e c t i o n p o i n t o f t h e

l i n e y = 1 w i t h c u r v e o f

y = 4 - 3 x^{2} . \Rightarrow 1 = 4 - 3 x^{2}

x = \pm 1 . v o l = π \int_{- 1}^{1} R {(x)}^{2} d x

w i t h R (x) = f (x) - 1 = 3 - 3 x^{2}

v o l = 2 π \underset{0}{\int^{1}} {(3 - 3 x^{2})}^{2} d x

v o l = 18 π \underset{0}{\int^{1}} (1 - 2 x^{2} + x^{4}) d x

= 18 π {[x - \frac{2}{3} x^{3} + \frac{1}{5} x^{5}]}_{0}^{1}

= 18 π [1 - \frac{2}{3} + \frac{1}{5}]

= 18 π [\frac{8}{15}] = \frac{144 π}{15}

Commented by john santu last updated on 23/Apr/20

Commented by jagoll last updated on 23/Apr/20

thank you

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