OpenStudy (dls):

Calculate Area bounded between:

4 years ago
OpenStudy (dls):

Curve \(\LARGE y^2(2a-x)=x^3\) and line \(\LARGE x=2a\)

4 years ago
OpenStudy (anonymous):

So integrate.

4 years ago
OpenStudy (dls):

@ganeshie8

4 years ago
ganeshie8 (ganeshie8):

@hartnn

4 years ago
ganeshie8 (ganeshie8):

can we simply integrate x=0 to 2a ?

4 years ago
ganeshie8 (ganeshie8):

\(\large \int_0^{2a} \sqrt{\frac{x^3}{2a-x}} dx\)

4 years ago
ganeshie8 (ganeshie8):

not getting ideas

4 years ago
hartnn (hartnn):

no, i don't think so i was thinking of trigonometric substitution first..to get polar forms of equation of curve

4 years ago
ganeshie8 (ganeshie8):

ohk..

4 years ago
hartnn (hartnn):

i am not able to graph/plot the curve...

4 years ago
ganeshie8 (ganeshie8):

yeah, a is there... we will get family of curves

4 years ago
ganeshie8 (ganeshie8):
4 years ago

ganeshie8 (ganeshie8):

a=1

4 years ago
hartnn (hartnn):

then \(\Large \large \int_0^{2a} \sqrt{\dfrac{x^3}{2a-x}} dx\) is correct

4 years ago
ganeshie8 (ganeshie8):

where to go frm here

4 years ago
ganeshie8 (ganeshie8):

wolfram says Standard computation time exceeded...

4 years ago
hartnn (hartnn):

http://www.wolframalpha.com/input/?i=integral+sqrt+%28+x%5E3%2F+%282a-x%29%29

4 years ago
hartnn (hartnn):

i can't imagine from where did he get this monstrous question...

4 years ago
ganeshie8 (ganeshie8):

oh wolfram solution looks neat, its subbing \(x = 2a sin^2\theta\)

4 years ago
ganeshie8 (ganeshie8):
4 years ago

ganeshie8 (ganeshie8):

thanks @hartnn i entered definite integral initially and it was giving up... http://www.wolframalpha.com/input/?i=int+0+to+2a+sqrt%28x%5E3%2F%282a-x%29%29

4 years ago
OpenStudy (dls):

i won't get internet connection to plot the curve .-.

4 years ago
OpenStudy (dls):

that was the main thing......

4 years ago
ganeshie8 (ganeshie8):

yeah, but its easy to visualize this particular curve

4 years ago
ganeshie8 (ganeshie8):

\(\large y = \sqrt{\frac{x^3}{2a-x}} \)

4 years ago
OpenStudy (dls):

Aapke options,apki screen par \[\LARGE 3 \pi a ^2\] \[\LARGE \frac{3 \pi a ^2 }{2}\] \[\LARGE \frac{3 \pi a^2}{4}\] \[\LARGE None ~\]

4 years ago
OpenStudy (dls):

i can hardly imagine where "pi" came from

4 years ago
ganeshie8 (ganeshie8):

pi comes in limits, after we sub x = 2a sin^2

4 years ago
OpenStudy (dls):

why are we subbing that ? :|

4 years ago
ganeshie8 (ganeshie8):

wolfram did that

4 years ago
OpenStudy (dls):

take minimum help of these things :/

4 years ago
ganeshie8 (ganeshie8):

wat things, wolfram solution doesnt make sense to u yet ?

4 years ago
ganeshie8 (ganeshie8):

see if below is any clear :- \(\large \int_0^{2a} \sqrt{\frac{x^3}{2a-x}}\) say \(x = 2a \sin^2 \theta\) x->0, \(\theta ->0\) x->2a, \(\theta ->\pi/2\) \(dx = 4a \sin \theta \cos \theta d\theta\) \(\large \int_0^{\pi/2} \sqrt{\frac{(2a\sin^2\theta)^3}{2a-2a\sin^2\theta}}\)

4 years ago