Question

definite integral from 0 to 24
x/(9+3x^(1/2)) I know the answer is 40 can someone just explain how to get the answer

Answer 1

Is the whole denominator in the square root?

\[\large \int_{0}^{24} \frac{x}{\sqrt{9 + 3x}}\]

Answer 2

it has to be if he wants an answer of 40

Answer 3

After checking, yes it must be

Yes thank you @Zarkon

Answer 4

yea sorry distracted by homework..the whole denominator is in the square root just as your showed

Answer 5

i was told the answer by a friend but i want to know how to do it so i understand similar problems in the future not just to simply get my hw done

Answer 6

\[I=\int\limits_{0}^{24}\frac{ x }{ \sqrt{9+3x} }dx\]
\[=\frac{ 1 }{ 3 }\int\limits_{0}^{24}\frac{ 3x }{ \sqrt{9+3x} }dx=\frac{1 }{ 3 }\int\limits_{0}^{24}\frac{ 9+3x-9 }{ \sqrt{9+3x} }dx\]
\[=\frac{ 1 }{ 3 }\int\limits_{0}^{24}\sqrt{9+3x}dx-3\int\limits_{0}^{24}\frac{ 1 }{ \sqrt{9+3x} }dx\]

Answer 7

im sorry but where does the 1/3 come from?

Answer 8

divide and multiply by 3 to make 3x in the numerator.

Answer 9

tmen add and subtract 9 to make 9+3x

Answer 10

ohh okay so you got rid of the 3 in the numerator with by dividing the 3?

Answer 11

correct.

Answer 12

okay thanks i think i got it :D

Answer 13

np