anonymous
  • anonymous
approximate the integral 0 to pi/2 xsin(x)dx by computing the Left and Right sums, using the parition (0, pi/6, pi/4, pi/3, pi/2).
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
approximate the integral 0 to pi/2 xsin(x)dx by computing the Left and Right sums, using the parition (0, pi/6, pi/4, pi/3, pi/2).
amistre64
  • amistre64
that doesnt appear to be a consistent partition
anonymous
  • anonymous
?

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anonymous
  • anonymous
that's ok, you're still adding areas of rectangles right?
amistre64
  • amistre64
each width needs to be calculated on it own merits; its not uniform across the interval
anonymous
  • anonymous
yes
amistre64
  • amistre64
find the values of f(x) at each point indicated by the partition
anonymous
  • anonymous
yeah
amistre64
  • amistre64
|dw:1333570749998:dw|
anonymous
  • anonymous
keep going please
amistre64
  • amistre64
determine the width of each interval|dw:1333570887385:dw|
anonymous
  • anonymous
alright
anonymous
  • anonymous
i got the left hand sum to be .6888 which is correct i just need the right
amistre64
  • amistre64
then i believe left sums are when the rectangle of area is at the height of the left dot |dw:1333570948653:dw| and the right sums are the areas of the rectangles at the right dot |dw:1333570989791:dw| and the sum of the areas is the approximation of the integral
amistre64
  • amistre64
pi/6 *sin(pi/6 )*pi/6 +pi/4*sin(pi/4)*(pi/4-pi/6)+pi/3*sin(pi/3)*(pi/3-pi/4)+pi/2*sin(pi/2)*(pi/2-pi/3) = 1.34 ... http://www.wolframalpha.com/input/?i=pi%2F6+*sin%28pi%2F6+%29*pi%2F6+%2Bpi%2F4*sin%28pi%2F4%29*%28pi%2F4-pi%2F6%29%2Bpi%2F3*sin%28pi%2F3%29*%28pi%2F3-pi%2F4%29%2Bpi%2F2*sin%28pi%2F2%29*%28pi%2F2-pi%2F3%29

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