Let $f$ be a polynomial with real coefficients. The integral $I _ { p , q }$ where $p < q$ is defined by $$I _ { p , q } = \int _ { p } ^ { q } ( f ( x ) ) ^ { 2 } - ( f ( | x | ) ) ^ { 2 } \mathrm {~d} x$$ Which of the following statements must be true? $1 I _ { p , q } = 0$ only if $0 < p$ $2 f ^ { \prime } ( x ) < 0$ for all $x$ only if $I _ { p , q } < 0$ for all $p < q < 0$ $3 \quad I _ { p , q } > 0$ only if $p < 0$ A none of them B 1 only C 2 only D 3 only E 1 and 2 only F 1 and 3 only G 2 and 3 only H 1, 2 and 3
..... 22
Let $f$ be a polynomial with real coefficients.
The integral $I _ { p , q }$ where $p < q$ is defined by
$$I _ { p , q } = \int _ { p } ^ { q } ( f ( x ) ) ^ { 2 } - ( f ( | x | ) ) ^ { 2 } \mathrm {~d} x$$
Which of the following statements must be true?
$1 I _ { p , q } = 0$ only if $0 < p$
$2 f ^ { \prime } ( x ) < 0$ for all $x$ only if $I _ { p , q } < 0$ for all $p < q < 0$
$3 \quad I _ { p , q } > 0$ only if $p < 0$
A none of them
B 1 only
C 2 only
D 3 only
E 1 and 2 only
F 1 and 3 only
G 2 and 3 only
H 1, 2 and 3