Question

Calculus Help
Fan + Medal

Answer 1

Did you sketch the region they are talking about ?

Answer 2

No. I dont understand how to.

Answer 3

this question was asked before here look around you might find it

Answer 4

Ganeshie answered it

Answer 5

I couldnt find it

Answer 6

this your region

Answer 7

but they have to be equal two equal areas

Answer 8

the total region is a triangle (you don't need calculus to figure its area is 8)
so you want a region with area of 4

you can use calculus to the the area up to x=a
integrate from 0 to a the area under the "curve" y=x

Answer 9

I got as far as finding the area being 4.

Answer 10

you want to find the area of lots of skinny rectangles from x=0 to x=a

Answer 11

one skinny rectangle has area = height*width = y dx
or, knowing y=x, x dx
now "add up" but in calculus, that means integrate
\[ \int x \ dx\]

Answer 12

1/2 x^2 +C

Answer 13

ok but what are the limits for x?

Answer 14

0 to 2 ?

Answer 15

0 to a (we don't know where a is, but we can still use it as the upper limit)

Answer 16

oh right

Answer 17

so you really want to do
\[ \int_0^a x \ dx = 4\]

Answer 18

it equals 4?? How?

Answer 19

the left side gives the area of the "small triangle" and the right side is ½ the area of the big triangle (you figured that out already)

Answer 20

OH! okay

Answer 21

I assume you can do the integral?

Answer 22

I got a^2/2

Answer 23

so you have the equation
\[ \frac{a^2}{2} = 4\]
solve for a

Answer 24

a= +- 2.82842712. So it would be 2.828

Answer 25

yes, looks good (we want the positive root)

Answer 26

Yay. Thank you!