Question

Can anyone help me with solving this integral?

Answer 1

\[\int\limits_{2}^{5} (4-2x)dx\]

Answer 2

which part is giving you night terrors?

Answer 3

lol the 2nd one!

Answer 4

what is the integration rule for x^n ?

Answer 5

\[\int\limits_{2}^{5} 4.dx - 2\int\limits_{2}^{5}x.dx\]

Answer 6

or you can think of it in terms of derivatives; what is the derivative rule for x^n ?

Answer 7

nx^n-1

Answer 8

good, now how would you undo that? which is all an integration is ... undoing a derivative

Answer 9

thats wht i am having trouble with!

Answer 10

divide by n and add 1 back to the exponent

Answer 11

\[x=x^1\]right?

Answer 12

x^1

Answer 13

yea

Answer 14

\[x^1=x^{2-1}\]so n=2 in this case

Answer 15

ohh yea right!

Answer 16

so, does x^2 derive down to 2x?

Answer 17

yea it will be 2x^2-1

Answer 18

but we need x!

Answer 19

but we already have a 2x

Answer 20

you dont HAVE to pull out the constant. In this case it acutally helps out

Answer 21

2x/2

Answer 22

\[\frac d{dx}x^2=2x\]
\[\int 2x~dx=x^2\]

Answer 23

ohh gotch yea so, its gona be like (5-2)^2

Answer 24

\[\int\limits_{2}^{5} 4.dx - \int\limits_{2}^{5}2x.dx\]
\[4x(5,2) - x^2(5,2)\]
\[[4(5)-4(2)] - [(5)^2-(2)^2]\]

Answer 25

so i was doing just 1 term of x

Answer 26

you were mixing up the subtraction and the function into an ungodly abomination :)

Answer 27

yea right, i got it now! Thank you very much.. :)

Answer 28

\[\int_{a}^{b} f(x)~dx=F(b)-F(a)~NOT~F(b-a)\]

Answer 29

-9

Answer 30

20-8-(25-4)

20-8-25+4

24 - 33 = -9 yes

Answer 31

yayy.. thanks again!