Question

HELP!!! Use the trapezoidal rule with n = 4 to approximate the area bounded by the curves y = sin2x, the lines x = 0, y = 0, and x = 1.

I. 0.277

II. 0.273

III. 0.555

IV. 1.109

V. 2.219

Answer 1

define the rule ...

Answer 2

average heights times width of partition

Answer 3

\[\frac{b-a}{n}\left(\frac{f(x_0)+f(x_1)}{2}+\frac{f(x_1)+f(x_2)}{2}+...+\frac{f(x_{n-1})+f(x_n)}{2}\right)\]
\[\frac{b-a}{2n}\left(f(x_0)+f(x_1)+f(x_1)+f(x_2)+...+f(x_{n-1})+f(x_n)\right)\]
\[\frac{b-a}{2n}\left(f(x_0)+2f(x_1)+2f(x_2)+...+2f(x_{n-1})+f(x_n)\right)\]

Answer 4

Still a little confused! Sorry...

Answer 5

find the values for the heights ...

sin(2(0))
sin(2(.25)) |
sin(2(.50)) | doubles these middle values
sin(2(.75)) |
sin(2(1))

and add em all up

Answer 6

is that sin(2x) or sin^2 (x) ??

Answer 7

sin^2(x)

Answer 8

http://www.wolframalpha.com/input/?i=%28sin%5E2%28%280%29%29%2B2sin%5E2%28%28.25%29%29%2B2sin%5E2%28%28.50%29%29%2B2sin%5E2%28%28.75%29%29%2Bsin%5E2%28%281%29%29%29%2F%282*4%29

Answer 9

0.277 is the answer! Thank you so much...!

Answer 10

the rule is defined in your material ... the hard part is keeping it all together tho

Answer 11

good luck

Answer 12

Thanks!