If $f\,\,\left( x \right)$ is a quadratic polynomial in x such that $6\,\,\mathop \smallint \limits_0^1 \,\,f\left( x \right)\,\,dx\,\, - \,\,\left\{ {f\left( 0 \right)\,\, + \,\,4f\,\,\left( {\frac{1}{2}} \right)} \right\} = k\,f\,\,\left( 1 \right)$, then $k = $

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Application +4 | -1

f\,\,\left( x \right)

is a quadratic polynomial in x such that

6\,\,\int \limits_0^1 \,\,f\left( x \right)\,\,dx\,\, - \,\,\left\{ {f\left( 0 \right)\,\, + \,\,4f\,\,\left( {\frac{1}{2}} \right)} \right\} = k\,f\,\,\left( 1 \right)

, then

k =

View answer and explanation

Correct option: C

\mathrm{1}

Option C (

\mathrm{1}

) is correct because when

f(x)

is a quadratic polynomial, the given equation holds true only when

k = 1

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