answer the challenge...

Question

anonymous · Answer

answered

amistre64 · Answer

this really isnt a chatbox; try to keep the conversation on a problem limited to the scope of the original post

anonymous · Answer

$$4\int\limits_{0}^{1}\int\limits_{0}^{\sqrt{1-x ^{2}}}\int\limits_{x ^{2}+2y}^{2-x}dz dy dx prove your answer$$

amistre64 · Answer

now i have to go find the other one to see if ishaan did good on it

anonymous · Answer

ಠ_ಠ

across · Answer

What is so tough about this mechanical problem?

amistre64 · Answer

coding it in latex apparently lol

anonymous · Answer

this problem needs understanding ... 2 yellow paper can answer it ...

amistre64 · Answer

all i have is white paper ....

across · Answer

It requires understanding? Are you kidding me? lol

anonymous · Answer

not lol im not joking

anonymous · Answer

hint is using triple integration... i know it is easy .... but it is a long process... it can be a challnge for you

across · Answer

$$\frac{1}{4}(7\pi-16)?$$

across · Answer

Prove that $\mathbb{Z}$ is isomorphic to the multiplicative group of rational numbers of the form $2^m$, where $m\in\mathbb{Z}$.

amistre64 · Answer

just becasue a process is long doesnt mean that is challanging.

amistre64 · Answer

$$4\int\limits_{0}^{1}\left(\int\limits_{0}^{\sqrt{1-x ^{2}}}\left(\int\limits_{x ^{2}+2y}^{2-x}dz\right) dy\right) dx$$

$$4\int\limits_{0}^{1}\left(\int\limits_{0}^{\sqrt{1-x ^{2}}}2-x-x^2-2y\ dy\right) dx$$

$$4\int\limits_{0}^{1}2\sqrt{1-x ^{2}}-x\sqrt{1-x ^{2}}-x^2\sqrt{1-x ^{2}}-{1-x ^{2}}\ dx$$

$$4\int\limits_{0}^{1}\sqrt{1-x ^{2}}(2-x-x^2)-{1-x ^{2}}\ dx$$

etc

amistre64 · Answer

$$4\int\limits_{0}^{1}\sqrt{1-x ^{2}}(2-x-x^2)-{1-x ^{2}}\ dx$$

$$4\int\limits_{0}^{1}\sqrt{1-x ^{2}}(2-x-x^2)\ dx+4(-{x-\frac{1}{3}x ^{3}}) $$

$$4\int\limits_{0}^{1}\sqrt{1-x ^{2}}(2-x-x^2)\ dx-\frac{16}{3} $$

and then int by parts whats left