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Home  >>  JEEMAIN and AIPMT  >>  Mathematics  >>  Class12  >>  Integral Calculus
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If $g(x) =\large\frac{f(x) +f(-x)}{2}$ defined over $[-3,3]$ and $f(x)=2x^2-4x+1$ then $\int \limits_{-3}^3=?$

\[\begin {array} {1 1} (a)\;0 \\ (b)\;42 \\ (c)\;24 \\ (d)\;36 \end {array}\]
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1 Answer

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$g(x) =\large\frac{f(x)+f(-x)}{2}$
$f(x) =2x^2-4x+1$
$f(-x) =2x^2+4x+1$
$\large\frac{f(x)+f(-x)}{2}$$=(2x^2+1)$
=> $ \int \limits_{-3}^3 g(x) dx$
=> $ \int \limits_{-3}^3 (2x^2+1) dx$
=> $ \bigg[ \large\frac{2}{3}x^3+x \bigg]_{-3}^3$
=> $\large\frac{2}{3}$$[x^3]+ \large\frac{2}{3}$$(-3)^3 + 3-(-3)$
=> $\large \frac{2}{3} $$[27+27]+6$
=> $ \large\frac{2}{3} $$\times 2 \times 27 +6$
=> $42$
Hence b is the correct answer
answered Dec 17, 2013 by meena.p
 

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