Mathematics

# $\displaystyle \int _{ 0 }^{ a }{ f\left( x \right) +f\left( -x \right) } dx$ is equal to

$\displaystyle \int_{-a}^{a}f (x)dx$

##### SOLUTION
Using property $\int _{ a }^{ b }{ f\left( x \right) dx } =\int _{ a }^{ b }{ f\left( a+b-x \right) dx }$,

we get
$\int _{ -a }^{ a }{ f\left( x \right) dx } =\int _{ 0 }^{ a }{ f\left( x \right) dx } +\int _{ 0 }^{ a }{ f\left( -a+a-x \right) dx } =\int _{ 0 }^{ a }{ f\left( x \right) dx } +\int _{ 0 }^{ a }{ f\left( -x \right) dx } =\int _{ 0 }^{ a }{ \left( f\left( x \right) +f\left( -x \right) \right) dx }$

$\int _{ 0 }^{ a }{ \left( f\left( x \right) +f\left( -x \right) \right) dx } =\int _{ -a }^{ a }{ f\left( x \right) dx }$

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Single Correct Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 86

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