Calculus

Question 1

How to do partial fracjtons

Answer 1

IF A REPEATED root in bottom, then must include repeated, non and other

If there is a Quadratic that can’t be fscforised, then partial fractions only work if you have order low / high by 1

So if it’s quad in bottom need ax +b / x2 to split !

Question 2

How to equate coeffeicmt of power to solve partial

Answer 2

Once you typically found first 2, then equate the coeffeicmt powers left and right together and you’ll find answer!
So 0 = A + c etc

Question 3

Once split up into partial how to integrate?

Answer 3

Split up fraction, now can integrate one by ln , one by standard result and can combine!

Question 4

How to integrate using complete the sqaure

Answer 4

Twke out thr fsctor first , because means less problems later

Then complete the square,

Identify a and x, remember X NOT NECESSAIRLY X don’t be stupid

Question 5

And when completimg the square, how to HALF?

Answer 5

Half the lower one only not the top one 😭

Question 6

Remmeber when making a trig sub how to do

Answer 6

1) look at table to find what trig sub to make
2) make sure ti make the fsctor si when squared gives same reuskt
3) now remember to do dx / theta = whatever, dx = whatver D THETA!

Now multiply
4) manipulate and integrate

5) convert back to x, thus use what you had originally, and also identities, then arcssin or whatever finally
+c!

Also if need tk bring something INTO a sqaure root, need to sqaure it first