Piecewise Function Integral

[laucha54321]

If a function is defined as f(x)=x+3 when x is between [-2;1] and f(x)=x²-4x+7 when x is between (1;3]. Shouldn't the integral be the sum between the integral of x+3 with the upper bound being 1 and the lower bound being -2 plus the limit when "a" approaches 1 from the right of the integral of x²-4x+7 with the lower bound being "a" and the upper bound being 3.

 

[AmandasMathHelp]

You don't need to bring limits into this... you should simply be doing integrals on both functions in their defined intervals. Is that what you meant?? Because if so then yes that would work

 

[pka]

See this LINK

 

[laucha54321]

I understand it's okay if I don't but what I mean is if it is wrong if I do. Because my math teacher told couldn't explain what was wrong with doing that.
Thanks for the reply

You don't need to bring limits into this... you should simply be doing integrals on both functions in their defined intervals. Is that what you meant?? Because if so then yes that would work

 

[laucha54321]

See this LINK

This is not what I am asking my problem is not with the actual math but how you write it. I know you can calculate when it is equal to one my question is if the domain of the function does not exist for x = 1 shouldn't it be the limit when x approaches that number? Thanks for the reply.

 

[HallsofIvy]

There is nothing "wrong" with doing it, just as there is nothing "wrong" with writing out the first 100 primes before doing the integral! It is just unnecessary and a waste of time.

 

[laucha54321]

There is nothing "wrong" with doing it, just as there is nothing "wrong" with writing out the first 100 primes before doing the integral! It is just unnecessary and a waste of time.

okay, so we can conclude that taking points of an exams for this would be unfair.

 

[HallsofIvy]

No, that's not what I said. It might be that the teacher wants the student to learn to avoid getting side-tracked and focus on what is relevant. In that case taking points off for doing unnecessary things, even if, eventually, you get the right answer, is perfectly reasonable.