Question

Find the value(s) of cc such that the area of the region bounded by the parabolae y=x^2−c^2 and y=c^2−x^2 is 576.576.
Answer (separate by commas): c=

Answer 1

@ganeshie8

Answer 2

start by sketching a rough diagram of the given curves and get a feel of the region whose area you seek

Answer 3

i have no clue how to do that for this

Answer 4

what are the given curves ?

Answer 5

they are simple paraboloe

Answer 6

y=x^2−c^2

can you sketch above parabola ?

Answer 7

sketch y = x^2
then pull it down by c^2 to get the graph y = x^2 - c^2

Answer 8

ok

Answer 9

good, similarly sketch the other curve also

Answer 10

y = c^2 - x^2

is same as y = -x^2 + c^2

first sketch y = -x^2, then push it up by c^2 units

Answer 11

@ganeshie8

Answer 12

Perfect! you seek the region between those curves

Answer 13

Notice that both the curves meet at their x intercepts.
Can you find the x intercepts ?

Answer 14

x=-1,1

Answer 15

Nope, x = -c, c

Answer 16

looks you have taken c = 1 when you graph

Answer 17

oh ok

Answer 18

Can you setup a definite integral for the required area ?

Answer 19

not sure how to;(

Answer 20

\(\int_a^b f(x)\,dx\)

gives the area between \(f(x)\) and \(x\) axis over the interval x = a and x=b.

Answer 21

we want to find the area between two curves over the interval x = -c and x = c

Answer 22

subtract the bottom curve from the top curve

Answer 23

Area between curves =
\[\int\limits_{-c}^c \text{(top curve)}- \text{(bottom curve)}\,dx\]

Answer 24

http://www.wolframalpha.com/input/?i=Integrate [%28c^2-x^2%29-%28x^2-c^2%29,{x,-c,c}]

Answer 25

What do i plug in to wolfram?

Answer 26

plugin below in woflram

Integrate[(c^2-x^2)-(x^2-c^2),{x,-c,c}]

Answer 27

(8c^3)/3

Answer 28

you want that to equal 576.576

Answer 29

(8c^3)/3 = 576.576

solve c

Answer 30

ok

Answer 31

ok got it :D