Determine a region whose area is equal to the given limit. lim_(n rightarrow infty) sum_(i=1)^n 2/n(5+(2i)/n)^(10)

Question

Determine a region whose area is equal to the given limit.

lim_{n \to \infty} \sum_{i = 1}^{n} \frac{2}{n} (5 + \frac{2 i}{n})^{10}

Answer 1

The limit is the area under the curve

t^{10}

between t=5 and t=7. The limit is over the n - th order Riemannian sum as arepresentation of the int 5 to

7 t^{10} d t

. h=2/n and

f (5 + 2 i / n) = f (x_{i})

.

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