Dinoduck94
New member
- Joined
- May 15, 2019
- Messages
- 22
I'm trying to understand 'Integration by Substitution' and there's one bit that I just can't wrap my head around.
If I use the following question as an example:
[math]\int x ~ e^{-x^2} dx [/math]
STEP 1
[math]u = -x^2 [/math][math]\dfrac{du}{dy} = -2x [/math]
STEP 2
[math]\dfrac{1}{2} \int e^u +C [/math]
STEP 3
[math]\dfrac{1}{2} * -e^{-x^2} +C [/math]
Answer:
[math]\int x ~ e^{-x^2} dx = - \dfrac{e^{-x^2}}{2} + C [/math]
The material that I have, explains everything except where the [math]\dfrac{1}{2}[/math] comes from, in Step 2 - and where the other 'x' term went (was it differentiated to 1?); and I'm just getting more confused the more I search online.
Can someone help with my understanding, please?
Thanks
If I use the following question as an example:
[math]\int x ~ e^{-x^2} dx [/math]
STEP 1
[math]u = -x^2 [/math][math]\dfrac{du}{dy} = -2x [/math]
STEP 2
[math]\dfrac{1}{2} \int e^u +C [/math]
STEP 3
[math]\dfrac{1}{2} * -e^{-x^2} +C [/math]
Answer:
[math]\int x ~ e^{-x^2} dx = - \dfrac{e^{-x^2}}{2} + C [/math]
The material that I have, explains everything except where the [math]\dfrac{1}{2}[/math] comes from, in Step 2 - and where the other 'x' term went (was it differentiated to 1?); and I'm just getting more confused the more I search online.
Can someone help with my understanding, please?
Thanks