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Romashka [77]
3 years ago
11

Any help would be great

Mathematics
1 answer:
STALIN [3.7K]3 years ago
6 0
Answer : 5 Celsius
Cause
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3 years ago
Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = 5 36 −
azamat

Answer: V = 193.25π

Step-by-step explanation: The method to calculate volume of a solid of revolution is given by an integral of the form:

V =  \pi\int\limits^a_b {[f(x)]^{2}} \, dx

f(x) is the area is the function that rotated forms the solid.

For f(x)=y= \frac{5}{36}-x^{2} and solid delimited by x = 2 and x = 4:

V = \pi\int\limits^4_2 {(\frac{5}{36}-x^{2} )^{2}} \, dx

V = \pi\int\limits^4_2 {(\frac{25}{1296}-\frac{10x^{2}}{36}+x^{4})  } \, dx

V = \pi(\frac{25.4}{1296}-\frac{10.4^{3}}{108}+\frac{4^{5}}{5}-\frac{25.2}{1296}+\frac{10.2^{3}}{108}-\frac{2^{5}}{5} )

V = \pi(\frac{50}{1296}-\frac{560}{1296}+\frac{992}{1296}   )

V = 193.25π

The volume of a solid formed by y = \frac{5}{36} - x^{2} and delimited by x = 2 and x = 4

is 193.25π cubic units.

6 0
3 years ago
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