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4 years ago

Integrate ∫cos²x sinx dx

Engineering

1 answer:

Marianna [84]4 years ago

3 0

Answer:

-⅓ cos³ x + C

Explanation:

∫ cos² x sin x dx

If u = cos x, then du = -sin dx.

∫ -u² du

Integrate using power rule:

-⅓ u³ + C

Substitute back:

-⅓ cos³ x + C

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3 years ago

Create a document that includes a constructor function named Company in the document head area. Include four properties in the C

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4 years ago

Describe the steps, tools, and technology needed in detail and

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Answer:

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3 years ago

"Carbon 14 (C-14), a radioactive isotope of carbon, has a half-life of 5730 ± 40 years. Measuring the amount of this isotope lef

igor_vitrenko [27]

Answer:

The age of the bones is approximately 14172 years.

Explanation:

The age of the bones can be determinated using the following decay equation:

$N_{(t)} = N_{0}e^{-\lambda t}$ (1)

<u>Where:</u>

N(t): is the quantity of C-14 at time t

No: is the initial quantity of C-14

λ: is the decay rate

t: is the time

First, we need to find λ:

$\lambda = \frac{ln(2)}{t_{1/2}}$

<u>Where:</u>

t(1/2): is the half-life of C-14 = 5730 y

$\lambda = \frac{ln(2)}{5730 y} = 1.21 \cdot 10^{-04} y^{-1}$

Now, we can calculate the age of the bones by solving equation (1) for t:

$t = \frac{-ln(\frac{N_{(t)}}{N_{0}})}{\lambda}$

We know that the bones have lost 82% of the C-14 they originally contained, so:

$N_{t} = (1 - 0.82)N_{0} = 0.18N_{0}$

$t = \frac{-ln(0.18)}{1.21 \cdot 10^{-04} y^{-1}}$

$t = 14172 y$

Therefore, the age of the bones is approximately 14172 years.

I hope it helps you!

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3 years ago

Someone claims that in fully developed turbulent flow in a tube, the shear stress is a maximum at the tube surface. Is this clai

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Answer:

Yes this claim is correct.

Explanation:

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4 years ago

Integrate ∫cos²x sinx dx​

Integrate ∫cos²x sinx dx