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dezoksy [38]
3 years ago
9

The arc of the parabola y = x^2 from (3,9) to (4,16) is rotated about the y-axis. Find the area of the resulting surface. Please

use Woframalpha only to check your final answer. Show all steps in solving the appropriate integral.
Mathematics
1 answer:
Hitman42 [59]3 years ago
8 0

Answer:

156.5

Step-by-step explanation:

Thinking process:

The area can be calculated using the formula:

S = \int\limits^4_3 {2\pi x\sqrt{1+}(2x)^{2} } \, dx

We let the substitution take place.

Therefore, we let u = 1 + 4x^{2}

Thus, du = 8dx.

So,

xdx = \frac{1}{8}du

Also, the interval of the integration changes to [ 37, 65]

Thus,

S = \int\limits^4_3 {2\pi \sqrt{1+4x^{2} } } \, dx \\= \int\limits^65_35 {2\pi \sqrt{\frac{1}{8}u } } \, dx

= \frac{1}{6} [ 65^{\frac{3}{2}-37^{\frac{3}{2} }  }

= 156.5 units²

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