Estimate the area under the graph of f(x)=1/x on [1,5] by dividing [1,5] into 4 equal subintervals and using right endpoints.

Expert Answers

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You need to remember that you may evaluate the area under a curve using the following summation such that:

`sum_(k=1)^n f(Delta x_k)*Delta x_k`

Since the problem provides the information that you need to divide the area under the curve into 4 equal subintervals, you may evaluate `Delta x_k`  such that:

`Delta x_k = (5-1)/4 => Delta x_k = 1 `

Since `Delta x_1 = Delta x_2 = Delta x_3 = Delta x_4 = 1`  and you need to use the right endpoints to approximate the area yields:

`A = f(1+1)*1 + f(2+1)*1 + f(3+1)*1 + f(4+1)*` 1

`A = (1/2)*1 + (1/3)*1 + (1/4)*1 + (1/5)*1`

`A = 1/2 + 1/3 + 1/4 + 1/5`

Bringing the fractions to a common denominator yields:

`A = (30+20+15+12)/60 => A = 77/60`

Hence, evaluating the area under the curve `f(x)=1/x`  using the division into 4 equal subintervals and the right endpoints, yields `A = 77/60` .

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