given-f-x-f-x-5-x-R-If-7-9-f-x-t-and-2-6-f-x-dx-t-2-4t-3-find-the-value-of-t-

Question Number 79419 by jagoll last updated on 25/Jan/20

given

f (x) = f (x + 5) \forall x \in R

If \int_{7}^{9} f (x) = t and \int_{2}^{6} f (x) dx =

t^{2} + 4 t - 3 . find the value of t .

Commented by jagoll last updated on 25/Jan/20

\underset{7}{\int^{9}} f (x - 5) d (x - 5) = t

\underset{2}{\int^{4}} f (x) dx = t \Rightarrow \underset{2}{\int^{6}} f (x) dx =

\underset{2}{\int^{4}} f (x) dx + \underset{4}{\int^{6}} f (x) dx = 2 t

therefore 2 t = t^{2} + 4 t - 3

t^{2} + 2 t - 3 = 0 {\begin{cases} t = - 3 \\ t = 1 \end{cases}

Commented by jagoll last updated on 25/Jan/20

Mr W, that right ?

Commented by john santu last updated on 25/Jan/20

i t h i n k w r o n g .

\underset{2}{\int^{6}} f (x) d x = \underset{2}{\int^{6}} f (x + 5) d (x + 5) =

\underset{7}{\int^{11}} f (x) d x = ? ?

Commented by mr W last updated on 25/Jan/20

{i t}^{'} s w r o n g s i r!

\underset{2}{\int^{6}} f (x) dx = \underset{2}{\int^{4}} f (x) dx + \underset{4}{\int^{6}} f (x) dx

= t + \underset{4}{\int^{6}} f (x) dx \neq 2 t

s i n c e \underset{4}{\int^{6}} f (x) dx \neq \underset{2}{\int^{4}} f (x) dx

Commented by mr W last updated on 25/Jan/20

a g a i n, i f T i s p e r i o d,

\int_{a}^{a + n T} f (x) d x = \int_{c}^{c + n T} f (x) d x f o r a n y a a n d c

b u t \int_{a}^{a + S} f (x) d x \neq \int_{c}^{c + S} f (x) d x i f S \neq n T a n d c \neq a + k T

Commented by jagoll last updated on 25/Jan/20

thanks you mister

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