If $g(x) = \frac{f(x) - f( - x)}{2}$ defined over $\lbrack - 3,3\rbrack$ and $f(x) = 2x^{2} - 4x + 1$, then $\int_{- 3}^{3}{g(x)dx}$ is equal to

Question

Dr. Abubacker · Accepted Answer

(a)
Given, $f(x) = 2x^{2} - 4x + 1$
$	herefore\ g(x) = \frac{2x^{2} - 4x + 1 - 2x^{2} - 4x - 1}{2} = - 4x$
$	herefore\int_{- 3}^{3}{g(x)dx} = - 4\int_{- 3}^{3}{x\ dx}$
$= - 4\left\lbrack \frac{x^{2}}{2} ightbrack_{- 3}^{3} = - 2\lbrack 9 - 9brack = 0$

Q. If $g(x) = \frac{f(x) - f( - x)}{2}$ defined over $\lbrack - 3,3\rbrack$ and $f(x) = 2x^{2} - 4x + 1$, then $\int_{- 3}^{3}{g(x)dx}$ is equal to

Explanation

Reviewed by Dr. Abubacker

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