- #1

- 13

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the integral is :

[tex]\[

I = \int\limits_0^1 {\int\limits_0^x {\int\limits_0^y {ydzdydx} } }

\][/tex]

I'm not sure about the answer , but i think it'll be

[tex]\[

\frac{{x^3 }}{3}

\][/tex]

am i right ??????

thanks

- Thread starter the one
- Start date

- #1

- 13

- 0

the integral is :

[tex]\[

I = \int\limits_0^1 {\int\limits_0^x {\int\limits_0^y {ydzdydx} } }

\][/tex]

I'm not sure about the answer , but i think it'll be

[tex]\[

\frac{{x^3 }}{3}

\][/tex]

am i right ??????

thanks

- #2

HallsofIvy

Science Advisor

Homework Helper

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- #3

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- #4

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I knew that i was wrong

Last edited:

- #5

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I am not so sure about that. I got a different answer. Perhaps you want to show your steps?

- #6

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[tex]\[

\begin{array}{l}

\int\limits_0^1 {\int\limits_0^x {\int\limits_0^y {ydzdydx = \int\limits_0^1 {\int\limits_0^x {\left( {\int\limits_0^y {ydz} } \right)} } } } } dydx = \int\limits_0^1 {\int\limits_0^x {y^2 } dydx} \\

= \int\limits_0^1 {\left( {\int\limits_0^x {y^2 dy} } \right)} dx = \int\limits_0^1 {\frac{{x^3 }}{3}} dx = \left( {\frac{{x^4 }}{{12}}} \right)_0^1 = \frac{1}{{12}} \\

\end{array}

\][/tex]

Thanks

- #7

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There you go.

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