Question

y=x^2 and y=sinx. Find the area using integration.

Answer 1

how would you know the interval? or the limit?

Answer 2

its that old equation again!

Answer 3

sorry.

Answer 4

x=0, 0.8767
you need to integrate both functions between these two limits and subtract
i'm assuming youe need the area between the two curves

Answer 5

i'm referring to x^2 = sin x

Answer 6

yes i do. but you got 0.8767 by using the graph?

Answer 7

- i got it on wolfram alpha! - the graph yes

Answer 8

our professor told us to get the value of the x using factorial. how do we do that?

Answer 9

oh i see - to be honest i dont know chakaron i'll have to check that out factorial or factoring?

Answer 10

one way would be is to draw the graph to get a rough figure then use trial and error until you get a more accurate answer but that is very tedious. using a calculator would speed it up.

Answer 11

its factorial. (e.g 5!=1x2x3x4x5) yes. I've tried the graph too but he said (professor) that it wouldn't be accurate.

Answer 12

For the integration of \[\int\limits_{0}^{1} (4-x2)dx \] what is the answer?

Answer 13

most trig functions can only be expressed by approximations

even when you know the power series you still cant determine its value since there are an infinite number of terms in the polynomial expressed

Answer 14

so there is no definite answer?

Answer 15

if you cant determine an exact answer for your bounds, then you will never be able to determine an exact area from it

Answer 16

your best bet would determine the level of accuracy that you want it to be

Answer 17

ok. thanks=)

Answer 18

its not possible to solve x^2=sinx without using a numerical method such as newton's method
and i'm pretty sure there are other methods as well

Answer 19

numerical methods dont provide an exact solution either :)

Answer 20

i mean it is easier to see x^2=sinx when x=0
but the other x you will need numerical approach

Answer 21

i know

Answer 22

but you can get close to the number

Answer 23

yes, close is as close gets ;)

Answer 24

there is a method called linear interpolation - a numerical method which will give you an answer to 4-5 decimal places reasonably quickly

Answer 25

so .8767 is pretty close

Answer 26

i guess so

Answer 27

use newton's method and chose intial guess 1
and did 5 iterations and got on the fifth iteration
.876741199
the first 4 number on the 4th iteration were the same
and i did do one more but i forgot to write it down the first 4 numbers were the same
so it seems to be getting pretty close to .8767

Answer 28

that s good - wolframalpha gave .876727