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Grade 11Integral Calculus

Let f be a real valued function satisfy
f(x) + f(x+4) = f(x+2) + f(x+6)
Prove that
limit (x to x+8)
∫f(t)dt is constant

Kawal

11 Years agoGrade 11

1 Answer

Jitender Singh

Approved Tutor Answer11 Years ago

Ans:Hello student, please find answer to your question
$f(x) + f(x+4) = f(x+2) + f(x+6)$ …..(1)
$f(x+2) + f(x+2+4) = f(x+2+2) + f(x+2+6)$
$f(x+2) + f(x+6) = f(x+4) + f(x+8)$ …......(2)
(1) + (2)
$f(x) = f(x+8)$
$I = \int_{x}^{x+8}f(t)dt$
$I' = f(x+8)-f(x)$
$I' = 0$
$\Rightarrow \int_{x}^{x+8}f(t)dt$
is constant

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