Question

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

Answer 1

\[\int\limits\frac{x}{4-x^{2}} dx\]?

Answer 2

use \frac{}{} for fractions

Answer 3

hehe. ok thanks. :)

Answer 4

can you solve @Mimi_x3 ? :)

Answer 5

easiest integral of 2012 ;D

Answer 6

let \(u= 4-x^2\) =>
\[\frac{du}{-2x} \]

Answer 7

\[\int\limits\frac{x}{4-x^{2}} dx => \int\limits\frac{\cancel{x}}{u} * \frac{du}{-2\cancel{x}} => -\frac{1}{2} \int\limits\frac{1}{u} du\]

Answer 8

\implies \(\implies\)

Answer 9

please substitute the value of u @Mimi_x3 . :)

Answer 10

you can do it beatles. just try.

Answer 11

I can't.
I can't do \[\frac{1}{2}\ln \frac{4}{7}\] is the answer. :(

Answer 12

the sub is \(u=4-x^2\) then you just sub it in..

Answer 13

but the answer on my book is what i type before. :(

Answer 14

wait its a definite integral; just sub in the limits

Answer 15

yeh his/her answer is right

Answer 16

\[-\frac{1}{2} \int\limits\frac{1}{u} du => -\frac{1}{2} \ln(u) + C => -\frac{1}{2} \ln(4-x^2) + C\]

Answer 17

will you do @Mimi_x3 ?

Answer 18

since wasiqs said that its right; then its right lol

Answer 19

by definite integration. :)

Answer 20

i feel honoured lol

Answer 21

wasiqs will do it for you. (:

Answer 22

@Mimi_x3 your answer is right if it is indefinite integration but in definite will you do it? see me the solution. :)

Answer 23

change the limits as you do the problem
\[u(x)=4-x^2\implies u(5)=4-5^2=-21\] etc

Answer 24

@Mimi_x3 are you sure that @wasiqss can do that? :)

Answer 25

then you don't have to convert back, you can leave everything in terms of \(u\)

Answer 26

ok thank you @satellite73 for your effort but I already know that but my solution can't get the correct answer. :(