Question

Approximate the area between the xxx-axis and h(x) = \dfrac{1}{7-x}h(x)= 7−x 1 ​ h, (, x, ), equals, start fraction, 1, divided by, 7, minus, x, end fraction from x = 2x=2x, equals, 2 to x = 5x=5x, equals, 5 using a left Riemann sum with 333 equal subdivisions.

Answer 1

Answer:

$\dfrac{47}{60}$ sq. units.

Step-by-step explanation:

The given function is

$h(x)=\dfrac{1}{7-x}$

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:

$Area=\sum_{n=0}^{N-1}f(x_n)(\Delta x_n)$

For given question,

$Area=\sum_{n=2}^{5-1}f(x_n)(\Delta x_n)$

$Area=\sum_{n=2}^{4}f(x_n)(\Delta x_n)$

$Area=f(x_2)(3-2)+f(x_3)(4-3)+f(x_4)(5-4)$

Now,

$Area=\dfrac{1}{7-2}\times (1)+\dfrac{1}{7-3}\times (1)+\dfrac{1}{7-4}\times (1)$

$Area=\dfrac{1}{5}+\dfrac{1}{4}+\dfrac{1}{3}$

$Area=\dfrac{12+15+20}{60}$

$Area=\dfrac{47}{60}$

Therefore, the required area is $\dfrac{47}{60}$ sq. units.