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3 years ago

What is the value of for the following data to three decimal places?

Mathematics

1 answer:

Ilya [14]3 years ago

4 0

Answer (B) is you answer

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Integral of x"2+4/x"2+4x+3

dolphi86 [110]

I'm guessing you mean

$\displaystyle \int\frac{x^2+4}{x^2+4x+3}\,\mathrm dx$

First, compute the quotient:

$\displaystyle \frac{x^2+4}{x^2+4x+3} = 1 + \frac{4x-1}{x^2+4x+3}$

Split up the remainder term into partial fractions. Notice that

<em>x</em> ² + 4<em>x</em> + 3 = (<em>x</em> + 3) (<em>x</em> + 1)

Then

$\displaystyle \frac{4x-1}{x^2+4x+3} = \frac a{x+3} + \frac b{x+1} \\\\ \implies 4x - 1 = a(x+1) + b(x+3) = (a+b)x + a+3b \\\\ \implies a+b=4 \text{ and }a+3b = -1 \\\\ \implies a=\frac{13}2\text{ and }b=-\frac52$

So the integral becomes

$\displaystyle \int \left(1 + \frac{13}{2(x+3)} - \frac{5}{2(x+1)}\right) \,\mathrm dx = \boxed{x + \frac{13}2\ln|x+3| - \frac52 \ln|x+1| + C}$

We can simplify the result somewhat:

$\displaystyle x + \frac{13}2\ln|x+3| - \frac52 \ln|x+1| + C \\\\ = x + \frac12 \left(13\ln|x+3| - 5\ln|x+1|\right) + C \\\\ = x + \frac12 \left(\ln\left|(x+3)^{13}\right| - \ln\left|(x+1)^5\right|\right) + C \\\\ = x + \frac12 \ln\left|\frac{(x+3)^{13}}{(x+1)^5}\right| + C \\\\ = \boxed{x + \ln\sqrt{\left|\frac{(x+3)^{13}}{(x+1)^5}\right|} + C}$

3 0

2 years ago

Can someone please help?

Fofino [41]

<h2>Your Answer should be:</h2>

134

120

would equal:

14.

5 0

2 years ago

Read 2 more answers

When you subtract a positive number from a negative number the difference is always

deff fn [24]

The answer is true.

(+)(+)= +

(-)(-)= +

(-)(+)= -

8 0

3 years ago

Macy’s sells 4 TVs for $680. How much would 7 TVs cost?

konstantin123 [22]

First, divide.

680 / 4 = $170 per TV

Second, multiply.

170 * 7 = $1,190

Best of Luck!

5 0

3 years ago

Read 2 more answers

Def is a right triangle if feel equals 24 and de equals 7 find df

makvit [3.9K]

-- If FE is the longest side in the right triangle, then
the length of the missing side is 22.956... (rounded).

-- If FE is not the longest side in the right triangle,
then the length of the missing side is 25 (exactly).

5 0

3 years ago