Question

Need some help with integration...

Answer 1

\[y = x ^{5}\sqrt{1-x ^{3}}\]

Answer 2

Split \(x^5\) into \(x^2 * x^3\), then put \(1-x^3 = u \)

Answer 3

Ah I will try this asap.

Answer 4

:) Take your time

Answer 5

Tag me when you are done... till then I will have a look at others' problems :)

Answer 6

cool thanx

Answer 7

just wanna make sure my steps are correct
\[x ^{3}.x ^{2}\sqrt{1-x ^{3}}\]
then through u substitution i get
\[-\frac{ 1 }{ 3 }\int\limits_{?}^{?}x ^{3}.\sqrt{u}.du\]
Is this correct so far?

Answer 8

Yeps :D

Answer 9

problem i have is i dont know how to get to the text books answer from there
books answer is
\[-\frac{ 2 }{ 9}(1-x^3)^{\frac{ 3 }{ 2 }} +\frac{ 2 }{ 15}(1-x^3)^{\frac{ 5 }{ 2 }}+c\]

Answer 10

No problem.. we got:

\[\int x^3. \sqrt{u} .du \]

Now, remember \(1 - x^3 = u \implies x^3 = 1- u\)

Answer 11

So, our integral will become:

\[\int (1-u). \sqrt{u} . du\]

Can you solve this integral?

Answer 12

Damn did not think of that. Let me check.

Answer 13

Sure

Answer 14

Is this correct?
\[(x - \frac{ u ^{2} }{ 2 }).\frac{ 2 }{ 3 }u ^{\frac{ 3 }{ 2 }}\]

Answer 15

When you are integrating only in terms of u... make sure that your result contains only u..

Answer 16

See... the integral will become...

\[\int (\sqrt{u} - \sqrt{u^3}).du \]

\[= u^{3/2}/(3/2) - u^{5/2}/(5/2) + C\]

\[= 2u^{3/2}/3 - 2u^{5/2}/5 + C\]

Answer 17

\[=2u^{\frac{3}{2}} (1 - u) + C\]

Answer 18

Now, just put u = 1 - x^3

Answer 19

Ah I see my mistake now. Thank you very much for your help.

Answer 20

:) Glad to be of help