Doubt from integration

#1

#2

Is it a?

#3

Ans:option c)
The main rule used:[x+14]=[x]+14

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#4

Iam so sry in final interval I made mistake and ans is a)[-14,-13)

#5

I did not understand your approach for I2(GIF waala) . Can you please explain

#6

We need to split the intervals so that the value of integrand (the function that need to be integrated )is constant in that particular interval.
Then split the integrals for each interval .
Replace the function with that constant value in each integral.
For ex:


Then each integral is that constant multiplied by x.

#7

We can also use the concept of taking constant out of integral(RHS) to find the value of LHS
{x/2}=1/2*{x}

#8

In last step how did you write fractional part of{x/2} as {x} /2

#9

Sry ignore that one(actually it came to be true for few cases and I believed it to be true for all cases but it’s wrong.
Sorry pls do ignore it