Question

try this one

if any one get answer
send me solution ​

Answer 1

$G(x) + G(x + \frac{1}{3} ) = 5$

Substituting x = x + ⅓

$G(x + \frac{1}{3} ) + G(x + \frac{2}{3} ) = 5$

Subtracting Both the equations

$G(x) = G(x + \frac{2}{3} )$

This concludes that the function is periodic with period of ⅔ .

Multiplying both sides with dx

$G(x)dx = G(x + \frac{2}{3} )dx$

Integrating both sides, from 0 to 1200.

I=$_{0}∫^{1200} G(x)dx = _{0} ∫ ^{1200} G(x + \frac{2}{3} )$

Adding both the terms

$2I = _0∫^{1200}( G(x) + G(x + \frac{1}{3} ))dx$

$2I = _{0}∫ ^{1200} 5dx$

$2I = 5(x)|_{0} ^{1200}$

$I = 3000$

So, the value of I/750 is accordingly:

$\frac{I}{750} = \frac{3000}{750} = 4$