Set up ʃ(subscript o)(superscript 1) x^4 dx as the limit of a Riemann Sum. Set up but do not evaluate ʃ(subscript 0)(superscript 1) x^4 dx as the limit of a Riemann Sum. You can choose...

 Set up ʃ(subscript o)(superscript 1) x^4 dx as the limit of a Riemann Sum.

 Set up but do not evaluate ʃ(subscript 0)(superscript 1) x^4 dx as the limit of a Riemann Sum. You can choose x(subscript i)(superscript *)  as right endpoints of the interval [x(subscript i),x(subscript i+1)].

Expert Answers
embizze eNotes educator| Certified Educator

Approximate `int_0^1x^4dx` using a Riemann sum:

The Riemann sum approximation is `sum_(i=1)^nf(x_i^"*")Deltax`

Now `Deltax=(1-0)/n=1/n`

Using right endpoints we get `x_i^("*")=0+i/n=i/n`

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`int_0^1x^4dx=lim_(n->oo)sum_(i=1)^n(i/n)^4(1/n)`

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