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Questions  >>  JEEMAIN and NEET  >>  Mathematics  >>  Class12  >>  Integral Calculus
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Q)

Integrate :$\int \limits_6^8 \large\frac{[x^2]}{[x^2-28 x +196]+[x^2]}$$ dx$

\[\begin {array} {1 1} (a)\;1 \\ (b)\;\frac{3}{4} \\ (c)\;4 \\ (d)\;3 \end {array}\]

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A)
$\int \limits_a^b \large\frac{f(x)}{f(a+b-x)+f(x)} $$dx=\large\frac{b-a}{2}$
$\int \limits_6^8 \large\frac{[x^2]}{[(-x+14)^2]+[x^2]}$$ dx$
$a+b =14$
$\large\frac{a-b}{2}=\frac{8-6}{2}$
$\qquad=1$
Hence a is the correct answer
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