Change of variable integral form

[Seeker555]

By making use of the change of variable y = x + 3 write the integral below in a form where the range of integration is \(\displaystyle [0,\infty ]\)

\(\displaystyle \int^{\infty}_{3}e^{-y}cos^2ydy\)

All I know to do is to substitute x + 3 into the integral where y is. I'd guess minusing 3 from the x + 3 could be what's required to have the integral in the form where the range is \(\displaystyle [0,\infty ]\) .

 

[Deleted member 4993]

By making use of the change of variable y = x + 3 write the integral below in a form where the range of integration is \(\displaystyle [0,\infty ]\)

\(\displaystyle \int^{\infty}_{3}e^{-y}cos^2ydy\)

All I know to do is to substitute x + 3 into the integral where y is. I'd guess minusing 3 from the x + 3 could be what's required to have the integral in the form where the range is \(\displaystyle [0,\infty ]\) .

You need to review your algebra!!

y = x+3

When y = 3 (the first limit of integration) how much is x? → 3 = x + 3 → 3 - 3 = x +3 - 3 → 0 = x

When y = ∞ (the second limit of integration) how much is x?

By the way, I am 99.37% sure that "minusing" is not a proper English word (although English is not my mother-tongue). The proper English and/or mathematical term - in the context - would be "subtracting".

 

[HallsofIvy]

By the way, I am 99.37% sure that "minusing" is not a proper English word (although English is not my mother-tongue). The proper English and/or mathematical term - in the context - would be "subtracting".

English is my native language and I am 100% sure that "minusing" is not an English word!

 

[Deleted member 4993]

English is my native language and I am 100% sure that "minusing" is not an English word!

I can never tell about you guys - you have "irregardless" as a dictionary entry.

That is why I had that 0.43% uncertainity....