23,579 38,743 65,559 +66.559

Mathematics

1 answer:

viktelen [127]2 years ago

5 0

Answer:

194,440 or 127,947.559

Step-by-step explanation:

if that's supposed to be a comma on 66.559 then the answer is 194,440. If not it's 127,947.559.

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∫(cosx) / (sin²x) dx

kirza4 [7]

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:

$\mathsf{sin\,x=u\quad\Rightarrow\quad cos\,x\,dx=du}$

and then, the integral (i) becomes

$=\mathsf{\displaystyle\int\! \frac{1}{u^2}\,du}\\\\\\
=\mathsf{\displaystyle\int\! u^{-2}\,du}$

Integrate it by applying the power rule:

$\mathsf{=\dfrac{u^{-2+1}}{-2+1}+C}\\\\\\
\mathsf{=\dfrac{u^{-1}}{-1}+C}\\\\\\
\mathsf{=-\,\dfrac{1}{u}+C}$

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: <em>indefinite integral substitution trigonometric trig function sine cosine cosecant sin cos csc differential integral calculus</em>

5 0

3 years ago

HELP ME! @all smart people

larisa86 [58]

The first one is 5.3 you multiply 4x4 which is 16 then divide by 3 which then gives you the answer

6 0

2 years ago

Read 2 more answers

Which equation is a point slope form equation for line AB? y−6=−2(x+2) y−2=−2(x+2) y−2=−2(x+6) y−2=2(x+2) A graph with a line ru

julsineya [31]

Answer:

y-6=-2(x+2)

Step-by-step explanation:

4 0

2 years ago

A line has a slope of zero and passes through the point (-2,6)

Lera25 [3.4K]

Answer:

y = 6

Step-by-step explanation:

If the slope of a line is zero, then it is a horizontal line. This means that the line will have a constant y value for all x, hence the equation of the line is y = 6

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2 years ago

What is the answer to this

NeX [460]

First equation answer:
(j= -7)
Second equation answer:
(j= 5)

4 0

3 years ago