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Home » Show thatf(x)g(x)dx=2f(x)g(x) are defined as f(x)=f(x-a) and g(x)+g(a-x)=4
Show that\int\limits_{\begin{smallmatrix} 0\\\end{smallmatrix}}^ {a}{{}}f(x)g(x)dx=2\int\limits_{\begin{smallmatrix} 0\\\end{smallmatrix}}^ {a}{{}}f(x)g(x) are defined as f(x)=f(x-a) and g(x)+g(a-x)=4
CBSE | Class 12 | Exercise 7.11 | Integrals | NCERT
Show that\int\limits_{\begin{smallmatrix} 0\\\end{smallmatrix}}^ {a}{{}}f(x)g(x)dx=2\int\limits_{\begin{smallmatrix} 0\\\end{smallmatrix}}^ {a}{{}}f(x)g(x) are defined as f(x)=f(x-a) and g(x)+g(a-x)=4

Since,  ……..(i)  and   ………(ii)

Let I =  ……….(iii)

 I = 

=  [From eq. (i)] ……….(iv)

Adding eq. (iii) and (iv)

2I = 

= 

 2I = 

[From eq. (ii)]

 2I = 

 I = 

 

i

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