2-6-x-1-x-2-x-3-x-9-dx-a-1-b-0-c-6-d-2-e-4-

Question Number 150247 by mathdanisur last updated on 10/Aug/21

\underset{2}{\int^{6}} (x - 1) (x - 2) (x - 3) \dots (x - 9) dx = ?

a) 1 b) 0 c) 6! d) - 2 e) 4!

Commented by amin96 last updated on 10/Aug/21

\int_{2}^{6} \underset{n = 1}{\prod^{9}} (x - n) d x = \underset{n = 1}{\prod^{9}} \int_{2}^{6} (x - n) d x =

= \underset{n = 1}{\prod^{9}} (∣_{2}^{6} (\frac{x^{2}}{2} - n x)) = \underset{n = 1}{\prod^{9}} (16 - 4 n) = 12 \cdot 8 \cdot 4 \cdot 0 \dots . = 0

Commented by mr W last updated on 10/Aug/21

m a y b e t h e q u e s t i o n i s

\underset{2}{\int^{8}} (x - 1) (x - 2) (x - 3) \dots (x - 9) dx = ?

Commented by amin96 last updated on 10/Aug/21

T h a n k s)

Commented by mathdanisur last updated on 10/Aug/21

T h a n k y o u s e r c o o l

Commented by mr W last updated on 10/Aug/21

o b v i o u s l y w r o n g!

\int_{a}^{b} f (x) g (x) d x \neq (\int_{a}^{b} f (x) d x) \times (\int_{a}^{b} g (x) d x)

Commented by mr W last updated on 10/Aug/21

a l l a n s w e r s g i v e n a r e w r o n g!

Commented by mr W last updated on 10/Aug/21

j u s t e x p a n d a n d {y o u}^{'} l l g e t t h e r i g h t

a n s w e r - \frac{1664}{5} .

Commented by mathdanisur last updated on 10/Aug/21

Thankyou Ser, so {what}^{'} s the solution now . ?

Commented by mr W last updated on 10/Aug/21

\underset{2}{\int^{8}} (x - 1) (x - 2) (x - 3) \dots (x - 9) dx = 0

Commented by mr W last updated on 10/Aug/21

\underset{5 - a}{\int^{5 + a}} (x - 1) (x - 2) (x - 3) \dots (x - 9) dx = 0

a \in R

Commented by mathdanisur last updated on 10/Aug/21

Thank You S er