given-function-f-x-f-x-2-for-x-R-if-0-2-f-x-dx-B-what-value-of-3-7-f-x-8-dx-

Question Number 77687 by jagoll last updated on 09/Jan/20

g i v e n f u n c t i o n

f (x) = f (x + 2) f o r \forall x \in R

i f \underset{0}{\int^{2}} f (x) d x = B, w h a t v a l u e o f

\underset{3}{\int^{7}} f (x + 8) d x = ?

Commented by mr W last updated on 09/Jan/20

\underset{3}{\int^{7}} f (x + 8) d x

= \underset{3}{\int^{7}} f (x + 4 \times 2) d x

= \underset{3}{\int^{7}} f (x) d x

= \underset{3}{\int^{7}} f (x - 3) d (x - 3)

= \underset{0}{\int^{4}} f (x) d x

= \underset{0}{\int^{2}} f (x) d x + \underset{2}{\int^{4}} f (x) d x

= \underset{0}{\int^{2}} f (x) d x + \underset{2}{\int^{4}} f (x - 2) d (x - 2)

= \underset{0}{\int^{2}} f (x) d x + \underset{0}{\int^{2}} f (x) d x

= 2 \underset{0}{\int^{2}} f (x) d x

\Rightarrow 2 B

g e n e r a l l y

i f f (x) = f (x + T) a n d \underset{0}{\int^{T}} f (x) d x = B,

\underset{a}{\int^{a + n T}} f (x + m T) d x = n \underset{0}{\int^{T}} f (x) d x = n B

w i t h n, m = i n t e g e r

Commented by jagoll last updated on 09/Jan/20

t h a n k s y o u s i r

Commented by jagoll last updated on 09/Jan/20

s i r W h o w a b o u t f (x) = f (x + 7) \forall x \in R

i f \underset{2}{\int^{4}} f (x) d x = 5 a n d \underset{3}{\int^{4}} f (x) d x = 2

w h a t i s \underset{9}{\int^{10}} f (x) d x = ?

Commented by mr W last updated on 09/Jan/20

\underset{9}{\int^{10}} f (x) d x

= \underset{9}{\int^{10}} f (x - 7) d (x - 7)

= \underset{2}{\int^{3}} f (x) d x

= \underset{2}{\int^{4}} f (x) d x - \underset{3}{\int^{4}} f (x) d x

= 5 - 2

= 3

Commented by jagoll last updated on 09/Jan/20

t h a n k s y o u s i r

Commented by jagoll last updated on 09/Jan/20

s i r l i n e 8 i s \underset{0}{\int^{2}} f (x) d x + \underset{0}{\int^{2}} f (x) d x . i s c o r r e c t s i r ?

Commented by jagoll last updated on 09/Jan/20

i t h i n k i t y o u r t y p o s i r

Commented by mr W last updated on 09/Jan/20

y e s, n o w f i x e d!

Facebook Tweet Pin