if-f-x-f-x-for-x-R-3-3-f-x-dx-0-2-3-f-x-dx-5-then-0-2-f-x-dx-

Question Number 125511 by sandy_delta last updated on 11/Dec/20

if :

f (x) = f (- x) for x \in R

\underset{- 3}{\int^{3}} f (x) dx = 0

\underset{- 2}{\int^{3}} f (x) dx = 5

then \underset{0}{\int^{2}} f (x) dx = ?

Commented by liberty last updated on 11/Dec/20

\Rightarrow \underset{- 3}{\int^{3}} f (x) d x = 2 \underset{0}{\int^{3}} f (x) d x = 0; \underset{0}{\int^{3}} f (x) d x = 0

\underset{- 2}{\int^{3}} f (x) d x = \underset{- 2}{\int^{0}} f (x) d x + \underset{0}{\int^{3}} f (x) d x

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

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

Commented by sandy_delta last updated on 12/Dec/20

thank you