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2 years ago

Integral of cosecx dx =log|tanx/2| show that.

Mathematics

1 answer:

Pie2 years ago

7 0

ANSWER:

Let t = logtan[x/2]

⇒dt = 1/ tan[x/2] * sec² x/2 × ½ dx

⇒dt = 1/2 cos² x/2 × cot x/2dx

⇒dt = 1/2 * 1/ cos² x/2 × cosx/2 / sin x/2 dx

⇒dt = 1/2 cosx/2 / sin x/2 dx

⇒dt = 1/sinxdx

⇒dt = cosecxdx

Putting it in the integration we get,

∫cosecx / log tan(x/2)dx

= ∫dt/t

= log∣t∣+c

= log∣logtan x/2∣+c where t = logtan x/2

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We need to find what g(-3) equals.

What the question is asking is what is the resulting value after you plug in -3 as n to the function. Meaning you replace the n that is in the function with -3.

g(-3) = $3( \frac{7}{5})^{-3}$

Remember back to the order of operations.

Parenthesis
Exponents
Multiplication
Division
Addition
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For this problem we can keep the fraction as it is (unless you are permitted to use a calculator... if that is the case then just plug all that into a calculator) and keep going to the exponent.

Negative exponents make fractions FLIP. So our fraction will look like this: $(\frac{7}{5})^{-3} = (\frac{5}{7})^{3}$

Now that we have it without the negative exponent we need to distribute the cubed power to each number in the fraction (which is essentially the same as saying this: $\frac{5}{7}* \frac{5}{7}* \frac{5}{7}$ )

$\frac{5^{3}}{7^{3}} = \frac{125}{343}$

We ARE NOT done! We still have this left:
g(-3) = $3 \frac{125}{343}$
Multiplying by 3 you get the following:

$\frac{375}{343}$

So what does g(-3) equal? This right here:

$\frac{375}{343}$

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3 years ago

Find the cube root of -8.

Lina20 [59]

Answer:

The cube root of -8 is -2

Step-by-step explanation:

Factor the numbers 8=2^3

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Apply radical rule;

∛2³=2

=-2

HOPE THIS HELPED!!!

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