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2 years ago

You make a salary of $500 a week and earn

Mathematics

1 answer:

Lelechka [254]2 years ago

4 0

$650. you get the 500 no matter what so x+500 we have to find 5% of 3000. $150 so, 500+150 is $650

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If you're using the app, try seeing this answer through your browser: brainly.com/question/2822772

_______________

Evaluate the indefinite integral:

$\mathsf{\displaystyle\int\! \frac{cos\,x}{sin^2\,x}\,dx}\\\\\\
=\mathsf{\displaystyle\int\! \frac{1}{(sin\,x)^2}\cdot cos\,x\,dx\qquad\quad(i)}$

Make the following substitution:

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$=\mathsf{\displaystyle\int\! \frac{1}{u^2}\,du}\\\\\\
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Integrate it by applying the power rule:

$\mathsf{=\dfrac{u^{-2+1}}{-2+1}+C}\\\\\\
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Now, substitute back for u = sin x, so the result is given in terms of x:

$\mathsf{=-\,\dfrac{1}{sin\,x}+C}\\\\\\
\mathsf{=-\,csc\,x+C}$

$\therefore~~\boxed{\begin{array}{c}\mathsf{\displaystyle\int\! \frac{cos\,x}{sin^2\,x}\,dx=-\,csc\,x+C} \end{array}}\qquad\quad\checkmark$

I hope this helps. =)

Tags: indefinite integral substitution trigonometric trig function sine cosine cosecant sin cos csc differential integral calculus

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