Question

Estimate the area under the graph of f(x)=1/x from x=1 to x=5 using for approximate rectangles and left endpoints?​

Answer 1

Step-by-step explanation:

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Answer 2

Given,

$\[f\left( x \right) = \frac{1}{x}\]$

Solution,

Calculate area under the graph from $\[x = 1\]$ to $\[x = 5\]$

Single integration represents area under the graph.

$\[ = \int\limits_{x = 1}^{x = 5} {\int {f\left( x \right)} } dx\]$

$\[ = \int\limits_{x = 1}^{x = 5} {\int {\frac{1}{x}} } dx\]$

$\[ = \left( {{\mathop{\rm lnx}\nolimits} } \right)_{x = 1}^{x = 5}\]$

$\[\begin{array}{l} = \ln 5 - \ln 1\\ = \ln 5\end{array}\]$

$\[ = 1.609\,uni{t^2}\]$

Hence the area under the graph is $\[ 1.609\,uni{t^2}\]$