_ - 4 ^4 ( 2^x + 2^ - x ) ( 3^x + 3^ - x ) ,dx is equal to - Vidyadip

MCQ

$\int\limits_{ - 4}^4 {\left( {{2^x} + {2^{ - x}}} \right)\left( {{3^x} + {3^{ - x}}} \right)} \,dx$ is equal to

A
$10$
B
$16\left( {\ln 2} \right)\left( {\ln 3} \right)$
C
$16\left( {\ln \frac{2}{3}} \right)$
✓
$0$

✓

Answer

Correct option: D.

$0$

d
$\left(2^{x}+2^{-x}\right)\left(3^{x}-3^{-x}\right)$ is an add function so

$\int_{-4}^{4}\left(2^{x}+2^{-x}\right)\left(3^{x}-3^{-x}\right) d x=0$

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