Changing limits in integration by substitution
When you change the limits according to the substitution and you end up with a lower number as a upper limit (i.e. 0) and a higher number as a lower limit (i.e. 2), do you just swap the two numbers and change the sign of the integral?
Original post by mp_x
When you change the limits according to the substitution and you end up with a lower number as a upper limit (i.e. 0) and a higher number as a lower limit (i.e. 2), do you just swap the two numbers and change the sign of the integral?
Yeah, from what I've learnt, you are supposed to always put the bigger number at the top
Original post by mp_x
When you change the limits according to the substitution and you end up with a lower number as a upper limit (i.e. 0) and a higher number as a lower limit (i.e. 2), do you just swap the two numbers and change the sign of the integral?
yes
Original post by cookiemonster15
Yeah, from what I've learnt, you are supposed to always put the bigger number at the top
Original post by M14B
yes
I guess what I meant to ask was why. Why must you change the sign of the integral when swapping the limits?
Original post by mp_x
When you change the limits according to the substitution and you end up with a lower number as a upper limit (i.e. 0) and a higher number as a lower limit (i.e. 2), do you just swap the two numbers and change the sign of the integral?
Well... it doesn't really make a difference, does it? You can certainly do that if you wish.
Original post by mp_x
I guess what I meant to ask was why. Why must you change the sign of the integral when swapping the limits?
To give you a positive answer
Original post by mp_x
I guess what I meant to ask was why. Why must you change the sign of the integral when swapping the limits?
Let's say integrates to , then you have and
Unparseable latex formula:
.\displaystyle[br]\begin{equation*}\int_b^a f(x) \, \mathrm{d}x = F(a) - F(b) = -(F(b) - F(a)) = -\int_a^b f(x) \, \mathrm{d}x\end{equation*}
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