A cylinder has a diameter of 12 centimeters and a height of 7 centimeters. Which formula below could be used to determine the lateral surface area of the cylinder?

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Ответ:

samtuck33

14.06.2020

Mathematics

a) $\pm 8\frac{x^{5}}{5}+C$

b) $\pm 4 sin(2x) + C$

Step-by-step explanation:

Given integrals are:

$a) \int\limits^a_b {\sqrt{{1+64x^{8}} } \, dx$ ---(1)

$b) \int\limits^a_b {\sqrt{1+64cos^{2}(2x)} } \, dx$ ---- (2)

Standard form

$L= \int\limits^a_b {\sqrt{1+(f'(x))^{2}} } \, dx$

Part A

compare (1) with standard form

$[f'(x)]^{2} = 64x^{8}\\f'(x)=\pm 8x^{4}\\f(x)= \pm8\frac{x^{5}}{5}+C$

Part B

Compare (2) with standard form

$[f'(x)]^{2}=64cos^{2}(2x)\\f'(x)= \pm 8cos(2x)\\f(x)=\pm 8\frac{sin(2x)}{2}+C\\f(x)= \pm 4sin(2x)+C$

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