Integral Calculus> please anyone help

please anyone help

milind , 10 Years ago

Grade 12

1 Answers

Jitender Singh

Last Activity: 10 Years ago

Ans:
Hello student,
Please find answer to your question below

[x] is the greatest integer that is less than or equal to x.

[x] is 0 if x lies between 0 (included) and 1 (excluded)
[x] is 1 if x lies between 1 (included) and 2 (excluded)

In this case, the xthterm is
$[\frac{3}{4}+\frac{x}{100}]$
where x varies from 0 to 99 (both included)
This will be equal to zero till the value inside is atleast 1.
Note that the last term is [3/4 + 99/100] = [1.74] = 1.
So every term will equal 1, starting from the term where 3/4+ x/100 = 1
$\frac{3}{4}+\frac{x}{100} = 1$
$x = 25$

Thus from x = 25, to x = 99, each term evaluates to 1.
And from x = 0 to x = 24, each term equal to zero.
So, the sum will be equal to: how many numbers are between 25 and 99 (both included) = 99 – 25 + 1 = 75