Question

Using 4 equal-width intervals, show that the trapezoidal rule is the average of the upper and lower sum estimates for the integral (see below).

Answer 1

\[\int\limits_{0}^{8} x ^{2}dx\]

Answer 2

So we know the intervals are going to be 0,2,4,6 and 8

Answer 3

@Michele_Laino

Answer 4

To find the trapezoidal area follow the formula:

A trapezoidal=(Δx/2)(y0+2y1+2y2+2y3+2y4+y5) where Δx=(b-a)/n

Answer 5

http://r.search.yahoo.com/_ylt=A86.J7osFjRVglAAq9knnIlQ;_ylu=X3oDMTEzMHQ3NXMwBHNlYwNzcgRwb3MDNQRjb2xvA2dxMQR2dGlkA1lIUzAwNF8x/RV=2/RE=1429505709/RO=10/RU=http%3a%2f%2fwww.jiskha.com%2fsearch%2findex.cgi%3fquery%3dLet%2bf%2528x%2529%2b%253D%2b4%2b%252D%2b%252E%2bCalculate%2bthe%2blower%2band%2bupper%2bsum%2bestimates%2bof%2bthe%2barea%2bunder%2bthe%2bcurve%2bover%2bthe%2binterval%2b%255B2%252C5%255D%2busing%2bsubintervals%2bof%2bwidth%2b%2526frac12%253B%252E/RK=0/RS=ffZkXPaZOYa.tM1nN90HmRD_xVI-

Answer 6

hold on love

Answer 7

do you have answer choices?

Answer 8

no

Answer 9

we have to compute the upper and lower sums

Answer 10

that is the lower sum