Mathematics

$$\int { n\sqrt { 1-{ n }^{ 2 } } dn }$$


SOLUTION
$$\int { n\sqrt { 1-{ n }^{ 2 } } dn } \quad 1-{ n }^{ 2 }=t$$
$$-2ndn=dt$$
$$ndn=\cfrac { -dt }{ 2 } $$
$$-\int { \cfrac { { t }^{ 1/2 }dt }{ 2 }  } =-\cfrac { 1 }{ 2 } \cfrac { { t }^{ 3/2 } }{ 3/2 } =\cfrac { -1 }{ 3 } { \left( 1-{ n }^{ 2 } \right)  }^{ 3/2 }$$
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Subjective Medium Published on 17th 09, 2020
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