Which is greater? 3/5, 33/50, 303/500, 3003/5000, 30003/50000

How do you integrate arctan(x dx? i think that if you simplify the integral you get:?

Temka [501]

Integration by parts will help here. Letting $u=\arctan x$ and $\mathrm dv=\mathrm dx$ , you end up with $\mathrm du=\dfrac{\mathrm dx}{1+x^2}$ and $v=x$ . Now

$\displaystyle\int\arctan x\,\mathrm dx=uv-\int v\,\mathrm du$
$\displaystyle\int\arctan x\,\mathrm dx=x\arctan x-\int\frac x{1+x^2}\,\mathrm dx$

For the remaining integral, setting $y=1+x^2$ gives $\dfrac{\mathrm dy}2=x\,\mathrm dx$ , so

$\displaystyle\int\frac x{1+x^2}\,\mathrm dx=\frac12\int\frac{\mathrm dy}y=\frac12\ln|y|+C=\frac12\ln(1+x^2)+C$

Putting everything together, you end up with

$\displaystyle\int\arctan x\,\mathrm dx=x\arctan x-\frac12\ln(1+x^2)+C$

6 0

2 years ago

Which polynomial is equivalent to 4n + 5^2

tankabanditka [31]

Answer:

16n^2+40n+25

Step-by-step explanation:

4 0

2 years ago

what equations best represents the problem? You drove for 425 miles at 60 mph. How long did it take you?

Kisachek [45]

If you drove for 425 miles at 60 mph, you would get there in 7 hours and 8-ish minutes. 425 divided by 60 is 7.08333333333333.

7 0

2 years ago

Read 2 more answers

Mai runs around a 400 meter track at a constant speed of 250 meters per minute. How many minutes does it take Mai to complete 4

goldfiish [28.3K]

Answer:

6.4 minutes, or 6 minutes and 24 seconds

Step-by-step explanation:

She is running 4 laps, so she is running 1600 meters total. If she runs 250 meters per minute, divide 1600 by 250 to determine how many minutes it will take...

1600/250 = 6.4

Which is 6 minutes + 0.4 minutes

*there are 60 seconds in a minute, so the 0.4 represents 40% of another minute. Multiply 60 by 0.4 to see how many seconds this is...

(0.4)60 = 24 seconds,

So she ran the laps in 6 minutes and 24 seconds

7 0

3 years ago

Read 2 more answers

Pam and Meg each have a picture frame. Pam’s picture frame is a square with an area of 3 square feet. Meg’s picture frame is a c

kondaur [170]

Answer:

The circumference of Meg’s picture frame is the perimeter of Pam’s picture frame by approximately 0.65 ft

Step-by-step explanation:

Pam's picture frame : Square with area of 3 sq. foot

Meg’s picture frame is a circle with a radius, r of 1 foot.

The circumference of Meg’s picture frame is the perimeter of Pam’s picture frame by approximately feet.

Let's calculate circumference of Meg's picture frame:

Circumference c, = 2πr

r = 1 ft

c = 2 * 3.14 *1 = 6.28 ft

Now calculate Perimeter of Pam's picture frame:

A is area of square and s is the side

A = s²

s² = 3

s = √3

Permeter of square = 4s

= 4√3 = 6.93ft

Now in order to find circumference of Meg’s picture frame is the perimeter of Pam’s picture frame, we have to find their difference.

Permimeter of square frame - Circumference of circle frame = 6.93 - 6.28 = 0.65

8 0

2 years ago