integrate gif

âˆ«(-100 to 100) [t³]dt

2 Answers

2305

Shaswata Roy ·2013-04-25 09:42:08

-100

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Hardik Sheth yeah....coz box x +box (-x)=(-)1...x not being an integer..
Upvote·0· Reply ·2013-04-25 11:31:29
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1357

Manish Shankar ·2013-04-26 07:00:55

(-100 to 0)âˆ«[t³]dt+(0 to 100)âˆ«[t³]dt

lets take the first part:
putting t=-x

(100 to 0)âˆ«[-x³](-dx)=(0 to 100)âˆ«[-t³]dt

Adding the two we get

I=(0 to 100) âˆ«{[t³]+[-t³]}dt

Now we know that [x]+[-x]=-1 when x is not an integer

so we will get the answer as -100

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