Question

Integration question

Answer 1

@ganeshie8 @yrelhan4

Answer 2

@mathstudent55

Answer 3

to clarify you want to take this integral and the [] indicate the the value is greater than the actual value?

Answer 4

hmm..greatest integer of [2.5] means 2..floor function

Answer 5

divide [x^2] top and bottom

Answer 6

nvm, it wont help..

Answer 7

\[\Large \int\limits_{4}^{10} \frac{dx}{1-\frac{28}{[x]}+\frac{16}{[x]^2} +1}\]

Answer 8

:/

Answer 9

that quadratic equation x^2-28x+196 will be = 0 when x=14 but that is out of our limits so I guess it wont be discontinuous in given integral limits ever so we won't have to worry about it maybe.

Answer 10

I think the way could be splitting the integration interval in parts for which the \([x^2]\) keeps constant. You see what I mean?

Answer 11

yep that is the only way so it will split into 6 integrals?

Answer 12

I would say way more

Answer 13

:O how more than that?

Answer 14

it's so complicated that im thinking there must be some trick to these!

Answer 15

yes, probably

Answer 16

I guess the longer way would be something like this:
\[\Large \int\limits_4^{5} \frac{16dx}{100+16}+ \int\limits_5^6 \frac{25dx}{81+25}+\int\limits_6^7+\int\limits_7^8+\int\limits_8^9+\int\limits_9^{10}\]