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Varvara68 [4.7K]

3 years ago

10

Your company insures snow removal operations. The snow removal premiums for each of the 3 years are $1,142 , $1,791 , and $2,003

. What was the total premium for the past 3 years?

1 answer:

trapecia [35]3 years ago

8 0

$1142 + 1791 + 2003 = 4936$
The answer is E.The total premium for the past 3 years is $4,936

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Now for partial fractions: you're looking for constants <em>a</em>, <em>b</em>, and <em>c</em> such that

$\dfrac{2x^2-7}{x(x^2+2)} = \dfrac ax + \dfrac{bx+c}{x^2+2}$

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$\dfrac{2x^2-7}{x(x^2+2)} = -\dfrac7{2x} + \dfrac{11x}{2(x^2+2)}$

Now, in the integral we get

$\displaystyle\int\frac{x^4+7}{x^3+2x}\,\mathrm dx = \int\left(x+\frac7{2x} - \frac{11x}{2(x^2+2)}\right)\,\mathrm dx$

The first two terms are trivial to integrate. For the third, substitute <em>y</em> = <em>x</em> ² + 2 and d<em>y</em> = 2<em>x</em> d<em>x</em> to get

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