Answer:
[tex]\dfrac{47}{60}[/tex] sq. units.
Step-by-step explanation:
The given function is
[tex]h(x)=\dfrac{1}{7-x}[/tex]
We need to find the area between x-axis and the given function from x=2 to x=5.
Left Riemann sum formula of area:
[tex]Area=\sum_{n=0}^{N-1}f(x_n)(\Delta x_n)[/tex]
For given question,
[tex]Area=\sum_{n=2}^{5-1}f(x_n)(\Delta x_n)[/tex]
[tex]Area=\sum_{n=2}^{4}f(x_n)(\Delta x_n)[/tex]
[tex]Area=f(x_2)(3-2)+f(x_3)(4-3)+f(x_4)(5-4)[/tex]
Now,
[tex]Area=\dfrac{1}{7-2}\times (1)+\dfrac{1}{7-3}\times (1)+\dfrac{1}{7-4}\times (1)[/tex]
[tex]Area=\dfrac{1}{5}+\dfrac{1}{4}+\dfrac{1}{3}[/tex]
[tex]Area=\dfrac{12+15+20}{60}[/tex]
[tex]Area=\dfrac{47}{60}[/tex]
Therefore, the required area is [tex]\dfrac{47}{60}[/tex] sq. units.
