Approximate the integral xsin(x) from 0 to pi/2 by computing L(f)P and U(f)P usi

Question

Approximate the integral xsin(x) from 0 to pi/2 by computing L(f)P and U(f)P using the partition (0, pi/6, pi/4, pi/3, pi/2). I've solved for L(f)P using: L=(pi/6)0+(pi/4-pi/6)0.2618+(pi/4-pi/3)(0.5554)+(pi/2-pi/3)0.9069= 0.6888 That's the correct answer. However, for the upper sum, U(f)P, I don't know how to solve it. I tried: U=(pi/4-pi/6)0.2618+(pi/3-pi/4)0.5444+(pi/2-pi/3)0.9069+ (pi/n)(1.5708). I don't know the last interval to multiply 1.5708 by, and I don't know how to input it into my online homework. My homework said I "May include a formula as an answer", but I don't know what formula to use. Any help would be appreciated, thanks. -Monica

Explanation / Answer

since we have partitions, our ?x will be the ; largest length of our partitions as the following:

p/6 - 0 = p/6 ===> largest
p/4 - p/6 = p/12
p/3 - p/4 = p/12
p/2 - p/3 = p/6 ===> largest

?x = p/6

Right hand sum:

p/2
? xsin(x)dx

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