Rotating the graph

Calculus Level 2

We have a function f ( x ) = x 2 ; 3 ≤ x ≤ 14 f(x) = x^2;\quad 3 \le x\le 14
V V is the volume of the object we get by rotating it's graph by the x x -axis.

If V = π × n V = \pi \times n what is n n equal to?


The answer is 107516.2.

Michal Pecho by Michal Pecho , 18, Slovakia

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1 solution

Michal Pecho
Mar 23, 2019

V = ∫ 3 14 π y 2 d x = ∫ 3 14 π x 4 d x = 14 5 π 5 − 3 5 π 5 V=\int _{ 3 }^{ 14 }{ \pi { y }^{ 2 } } dx = \int _{ 3 }^{ 14 }{ \pi { x }^{ 4 } } dx = \frac { { 14 }^{ 5 }\pi }{ 5 } -\frac { { 3 }^{ 5 }\pi }{ 5 }

V = π × n ⇒ π × n = 14 5 π 5 − 3 5 π 5 V=\pi \times n \Rightarrow \pi \times n=\frac { { 14 }^{ 5 }\pi }{ 5 } -\frac { { 3 }^{ 5 }\pi }{ 5 }

π × n = π ( 14 5 5 − 3 5 5 ) \pi \times n=\pi \left( \frac { { 14 }^{ 5 } }{ 5 } -\frac { { 3 }^{ 5 } }{ 5 } \right)

n = 14 5 5 − 3 5 5 n=\frac { { 14 }^{ 5 } }{ 5 } -\frac { { 3 }^{ 5 } }{ 5 }

n = 107516.2 n=107516.2

3 Helpful 1 Interesting 2 Brilliant 0 Confused

thiz boii iz rilly ztupid

Ban anán - 2 years, 2 months ago

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