Question

Use the method of quadrature to estimate the area under the curve y=-x^2+5 and above the x-axis from x = 0 to x = 2.
a.
7
c.
5
b.
14
d.
28

Answer 1

whats method of quadrature ?

Answer 2

The word quadrature has (at least) three incompatible meanings. Integration by quadrature either means solving an integral analytically (i.e., symbolically in terms of known functions), or solving of an integral numerically (e.g., Gaussian quadrature, Newton-Cotes formulas). Ueberhuber (1997, p. 71) uses the word "quadrature" to mean numerical computation of a univariate integral, and "cubature" to mean numerical computation of a multiple integral.
http://mathworld.wolfram.com/Quadrature.html

Answer 3

I kinda still don't know what it means. :p

Answer 4

Ahh so we just need to count the number of squares in the region of interest ?

Answer 5

are you serious? that means you have to draw a perfect or somewhat perfect graph

Answer 6

not really @freckles

Answer 7

lol

Answer 8

http://en.wikipedia.org/wiki/The_Quadrature_of_the_Parabola
Is this what you are talking about?

Answer 9

that looks interesting

Answer 10

9 months ago @ganeshie8 encountered a similar problem http://openstudy.com/study#/updates/5350f6a1e4b0b39169cd9e18

Answer 11

yeah id rather count squares for appoximation
but this requires graphing..

Answer 12

psst... @imbatman03

Answer 13

hehe

Answer 14

counting squares is easy
i just don't see how this is a good method for people are horrible at drawing like me

Answer 15

Something is seriously wrong with the education system. Why call counting squares the "method of quadrature"?

Answer 16

they mostly would have a graph inserted with the question ;)

Answer 17

lol ikram :P

Answer 18

i prefer the phrase `method of squares/boxes`.. but i guess there must be historical reasons for using the word quadrature

Answer 19

because of some proof that Archimedes proved the area of a parabola is equivalent to this series :-
sum 1/2^n