Question

determine which of the integrals can be
found using the basic integration formulas you have studied
so far in the text.

Answer 1

@mathsmind idk how to write this one on here

Answer 2

but heres the link to it http://learn.flvs.net/educator/temp/atucker69/2579/ChapterFive/5.07.pdf

Answer 3

its 48 and 50

Answer 4

\[y = e^{x^{2}}\]

Answer 5

for part (a) you can't use basic elementary methods to integrate this function, you need to travel from the Cartesian world and migrate to polar's world

Answer 6

okay

Answer 7

for part be you can use elementary way if and only if you multiply by 2/2

Answer 8

in other words we know that \[\frac{ dy }{ dx }= 2xe^{x^{2}}\]

Answer 9

\[\frac{ 1 }{ 2 } \int\limits2 xe^{x^{2}}\]

Answer 10

but still you can't use an elementary way to integrate, all we did is we depended on the driveler in order to figure out the integral

Answer 11

the other reason would be this is an erf error function which is beyond the scope of the level you are at

Answer 12

for part c this would be an Ei system again this is not elementary

Answer 13

Ei waaa? lol

Answer 14

you don't wanna know that one, trust me! hehehe

Answer 15

ok let's move on to question 50

Answer 16

lol okay

Answer 17

ive never heard that one before

Answer 18

now question 50 part a because the denominator is greater than the numerator we use integration by parts

Answer 19

hold on let me go understand 48 first

Answer 20

for part (b) you would get an arctan(x^2) just look at the substitution

Answer 21

well i think all you have to say for question 48 is no it can't be solved the elementary way because it does not include its derivative, or any elimination factor for simplification, that is why using the usual methods would be useless...

Answer 22

okay thanks now im ready for 50

Answer 23

for question 50

Answer 24

50(a) you would get aln(.../...) +barctan(...)+darctan(...)+c

Answer 25

you will be using some factorizing technique then apply partial fraction...

Answer 26

for 50(b) using the u sub you'll get bartan(x^2)+c

Answer 27

for part 50(c) you would get a natural log, aln(1+x^4)+c, this is because we have the derivative at the numerator of the function in the denominator ...

Answer 28

50(b) barctan(x^2)+c

Answer 29

okay im gonna look at it

Answer 30

finishing one more on that section

Answer 31

which one i did a b and c

Answer 32

ik i said im finishing one more question for that section then ill look at 50

Answer 33

oh ok...

Answer 34

ok i will go and play a game

Answer 35

lol thanks to you i actually finished chapter 5 in one day !

Answer 36

chapter 6 is only 3 sections almsot done with the course !

Answer 37

almost*

Answer 38

you are welcome!

Answer 39

what is chapter 6 about?

Answer 40

is this your final exam or something?

Answer 41

lol no this is my calculus course that im taking online i need to finish it in march to graduate, which is why im speeding and doing math all day everyday lol

Answer 42

ok good luck what is the next topic then!

Answer 43

chapter 6 is Differential Equations im trying to get it done today then i have to finish chapter 7 which is two section and chapter 8 is my last chapter but i already finished it, i have 3 more sections on chapter 4 then im done !! except the test but that wont take much time (:

Answer 44

ok

Answer 45

yup im going to do 50 now

Answer 46

dy/dx=x-y

Answer 47

, find the indefinite integral