Question

plase solve and explain the question ill post to down :

Answer 1

\[\int\limits_{}\sqrt{x}\sqrt{a^{2}x^{2}}dx\]

Answer 2

ax.sqrt(x) dx; u = sqrt(x); u^2 = x; 2u du = dx ..... maybe

a.u^2.u.2u.du

Answer 3

{S} 2a.u^4.du ; the 2a acts like a constant perhaps?

\[\frac{2au^5}{5}\]

Answer 4

u^5 = u^2.u^2.u = x.x.sqrt(x)

\[\frac{2a}{5}x^2\sqrt{x}+C\]
maybe

Answer 5

maybe :)

Answer 6

it works lol

Answer 7

u took u = sqrt(x) so that it been u^2*a*u ^^ then its u^3*adx

Answer 8

\[\frac{2a}{5}*(2x\sqrt{x}+\frac{x^2}{2\sqrt{x}})\]

Answer 9

why isnt \[\sqrt{x}\times \sqrt{x^3}=x^2\]?

Answer 10

and du =u^2 so its now u^3.a.u^2 then its u^5.a / 5 + c

Answer 11

if the problem says (my eyes not what they ought to be)
\[\int\sqrt{x}\sqrt{a^2x^3}dx\] then isnt this the same as
\[a\int x^2 dx\]?

Answer 12

just get
\[\frac{ax^3}{3}\] and be done

Answer 13

nono its X^2 not X^3 in this sqrt :D

Answer 14

\[\frac{2a}{5}(\frac{4x^2+x^2}{2\sqrt{x}})=\frac{2a}{5}(\frac{5x^2}{2\sqrt{x}})\]
\[2a(\frac{x^2\sqrt{x}}{2x})=a(x\sqrt{x})=ax\sqrt{x}\]

Answer 15

ooooooooooooooh sorry

Answer 16

i think its \[a*u^{5}/5\]

Answer 17

and + C

Answer 18

its:
2a x^5
------ +C :)
5

Answer 19

then i believe you get
\[\frac{2a}{5}\sqrt{x^5}\]

Answer 20

amistre root over the
\[x^5\]

Answer 21

2 ?? where this 2 came from ?? i thought that dx was du^2

Answer 22

forget u and du etc

Answer 23

just rewrite w/ exponents and use power rule

Answer 24

\[\sqrt{x}\sqrt{a^2x^2}=\sqrt{a^2}x^{\frac{3}{2}}\]

Answer 25

hmm , why u don't get a^2 out of the swrt?

Answer 26

hmm , why u don't get a^2 out of the swrt?

Answer 27

because it is always possible that a < 0

Answer 28

and i don't want to fret about rewriting as |a|

Answer 29

wel but ^2 always will equal to +

Answer 30

so i left it in the redical

Answer 31

exactly. which is why i cannot pull it out

Answer 32

because if i write it as
\[a x^{\frac{3}{2}}\] this would be incorrect if say a = -3

Answer 33

satalllite i think its easier to define ıu and du :D

Answer 34

what?

Answer 35

just have
\[\int x^{\frac{3}{2}}dx=\frac{2}{5}x^{\frac{5}{2}}\] finish

Answer 36

well its goo dtoo :D

Answer 37

just use power rule that is all. but of course you are free to use whatever

Answer 38

thanks :D