Mathematics

# $\displaystyle \int_{0}^{1}x\left ( 1-x \right )^{4}dx= \frac{1}{C}$, then $C=?$

30

##### SOLUTION
Let $\displaystyle I=\int _{ 0 }^{ 1 } x\left( 1-x \right) ^{ 4 }dx$
Using $\int _{ a }^{ b }{ f\left( x \right) dx } =\int _{ a }^{ b }{ f\left( a+b-x \right) dx }$
$\displaystyle \therefore I=\int _{ 0 }^{ 1 } \left( 1-x \right) x^{ 4 }dx=\int _{ 0 }^{ 1 } \left( x^{ 4 }-x^{ 5 } \right) dx=\frac { 1 }{ 5 } -\frac { 1 }{ 6 } =\frac { 1 }{ 30 }$

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One Word Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 111

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