Question

Please help? Will FAN AND MEDAL!

Find the range of the function f of x equals the integral from negative 6 to x of the square root of the quantity 36 minus t squared dt.

a. [-6,0]
b. [0,6]
c. [0,9pie]
d. [0,18pie]

Answer 1

Can you please help? @zepdrix @Directrix @Nnesha @agent0smith

Answer 2

You gotta take screenshots or learn to use latex.

Answer 3

what is latex?

Answer 4

The equation writing on here, press the equation button and start learning. Screenshots too. Don't write integrals in words, good god no.

Answer 5

\[f(x)=\int\limits_{-6}^{x}\sqrt{36-t^2}dt\]

Answer 6

I'd start by drawing the function inside the integral. The sqrt(36-t^2).

Hopefully you recognize it as a semicircle

Answer 7

Remember that the integral means you're finding the area under the curve.

If you drew out that semicircle, what is the area of it?

Answer 8

\[\sqrt{-(t+6)(t-6)}\]
I put the original equation in and got this

Answer 9

@agent0smith

Answer 10

That has nothing to do with what i said though...

Answer 11

I dont understand how to draw the semi-circle, or how to find the area? That is why I put that into my calculator because that is what I thought you were suppose to do.

Answer 12

Draw means graph.

Answer 13

okay so graph the equation

Answer 14

Once you realize it's a semicircle and find the radius, finding the area is easy.

Answer 15

Look. Find the radius. Then find the area.

https://www.google.com/search?q=y%3Dsqrt(36-x%5E2)&oq=y%3Dsqrt(36-x%5E2)&aqs=chrome..69i57&sourceid=chrome&ie=UTF-8

Answer 16

Okay the radius is either -5.4 or 5.4

Answer 17

Sorry -5.66 or 5.66

Answer 18

Look at the graph i gave.

Answer 19

And... a radius is a length.... they can't be negative.

Answer 20

Okay the radius is 6

Answer 21

so the area is \[36\pi \]

Answer 22

The area of a circle of radius 6 is 36pi. This is not a circle.

Answer 23

I know it is a semi-circle so it half of that. So the area is 18pi.

Answer 24

So if you integrated that function from x = -6 to x = 6, that's the area of the entire semircircle

If you integrated from x=-6 to x=-6, what would the area be?

Answer 25

9pi.?

Answer 26

If you integrate any function from x=a to x=a, the area is always the same value.

Answer 27

\[\Large \int\limits_a^a f(t)dt= 0\]

Answer 28

Okay so it would be D. [0,18pi]

Answer 29

@agent0smith

Answer 30

I gave you a medal right after your last post for a reason

Answer 31

Ohh it never said you did. I'm sorry.

Answer 32

Thank you for the help.

Answer 33

You're welcome.