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lisov135 [29]
3 years ago
7

Y = 3 sin2x, y = 0, 0 ≤ x ≤ π; about the x−axis

Mathematics
1 answer:
Dominik [7]3 years ago
8 0
I assume you're revolving the region with those bounds about the x-axis, and supposed to find the volume.

Via the disk method,

\displaystyle\pi\int_0^\pi(3\sin2x)^2\,\mathrm dx=9\pi\int_0^\pi\sin^22x\,\mathrm dx

Recall the half-angle identity for sine:

\sin^2t=\dfrac{1-\cos2t}2
\implies\displaystyle\frac{9\pi}2\int_0^\pi(1-\cos4x)\,\mathrm dx
=\displaystyle\frac{9\pi}2\left(x-\frac14\sin4x\right)\bigg|_{x=0}^{x=\pi}
=\dfrac{9\pi^2}2
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Complete question:

Joelwants to buy a new tablet computer from a store having a 20% off sale on all tablet. The tablet he wants has an original cost of $190. He also wants to make sure he has enough money to pay the 5% sales tax.

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Step-by-step explanation:

Given the following :

Sales tax = 5%

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Joel's incorrect expression : 0.95(190)(0.8)

Joel's mistake is the 0.95 which is equivalent to 95% used in Calculating the total cost of the computer. The sales tax increases the total cost of the computer and instead of subtracting 5% sales tax, it should be added.

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1 - 0.2 = 0.8

5% sales tax = 0.05 will be added :

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Therefore,

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