Question

Can someone explain how we use an integral to find the area?

Answer 1

This is a circle or a sphere?

Answer 2

Hey ishaan

Answer 3

It is a circle

Answer 4

I knwo the steps but I dont get what i am doing

Answer 5

Where is the trouble? ..also is any information given regarding this chord? .. what angle it suspends .. and is the width of the chord comparable to the radius?

Answer 6

nooo just show some arrows and a h

Answer 7

Have you discussed polar integration yet? I doubt it, but just to be sure.... -.-

Answer 8

no

Answer 9

like the book used pythagorean theroem in the begginning. in order to get the equation of the integral

Answer 10

I guess everybody fell asleep at the comp like me -_-

Answer 11

No, but it seems rivermaker is typing a very length reply, so I was waiting to see ;)

Answer 12

lengthy*

Answer 13

hehe I was just teasing :D

Answer 14

river are you still going, or is it saying you're typing by mistake?? haha

Answer 15

Let us take any function y = f(x)
THe area under the curve y = f(x) is the sum of rectangular strips (like one shown near rhe middle of the picture)
if you assume the co-ordinates of the strip as \[(x_{0}, 0), (x_{0}, y_{0}), (x_{1}, y_{1}), (x_{1},0) \]
then the area of the strip is approximated by \[y_{0} \times (x_{1} - x_{0}) \]
So the area under the curve is the sum of such strips
\[\sum_{x=a}^{x=b}f(x) \Delta x, \]
where \[\Delta x \] is the width of the strip at \[x\]
Going to the limit as \[\Delta x \rightarrow 0, \]
we get the area as \[\int\limits_{a}^{b} f(x) dx\]