Having trouble with the 2nd integration part
#Calc 2 Integration by parts
stuck pilot
grizzled daggerBOT
Having trouble with the 2nd integration part
- Wait patiently for a helper to come along.
- Once someone helps you, say thank you and close the thread with:
+close
- Feel free to nominate the person for helper of the week in #helper-nominations
- Do not ping the mods, unless someone is breaking the rules.
- If you're happy with the help you got here, and the server overall, you can contribute financially as well:
tawny torrent
Having trouble with the 2nd integration part
let the integral you want to evaluate =I, then integrate by parts twice and solve for I
stuck pilot
use tabular integration
what is tabular integration
steady vale
Hallelujah
its basically just a way to set up integration by parts
it looks nice and is fast
lemme make a diagram
or not
so essentially you have two columns
u and v
u for differentiating and v for integrating
as for integration by parts, to determine what u and whats v, use liate (logs, inverse trig, algebra, trig, exponential) or lipet (logs, inverse, polynomial, exponential, trig)
whatever comes first is your u and other is v
here we have an exponential and a trig function, so we could do either, but importantly we should realize that these can be differentiated and integrated forever, but we can resolve this
so first we have
e^4x sin5x
differentiate left and integrate right
4e^4x. -1/5cos5x
nothing cancels out or is repeated so again
16e^4x. -1/25sin5x
and there we see we have the original * a coefficient
for tabular you take diagonal multiples in alternating signs
so we take the first e^4x and multiply by -1/5cos5x and leave it positive
then add the next diagonal: 4e^4x * -1/25sin5x but we multiply by -1
and lastly we can multiply across for 16e^4x * -1/25sin5x, but since its across its still in an integral
im rambling
do u wanna just hop in a vc and i can screenshare?
steady vale
kinda we have to use a trick
stuck pilot
yeah im down for a vc
