QJEEAdv06Mac587: JEE Advanced 2006 Mathematics - Class 12 JEEAdv06Mac587 Solution: Let the definite integral be defined by the formula For more…

Question

Verified Solution • 2025–26 Session moderate

Let the definite integral be defined by the formula

\int\limits_a^b {f\left( x \right)dx = {{b - a} \over 2}\left( {f\left( a \right) + f\left( b \right)} \right).}

For more accurate result for

c \in \left( {a,b} \right),

we can use

\int\limits_a^b {f\left( x \right)dx = \int\limits_a^c {f\left( x \right)dx + \int\limits_c^b {f\left( x \right)dx = F\left( c \right)} } }

so
that for

c = {{a + b} \over 2},

we get

\int\limits_a^b {f\left( x \right)dx = {{b - a} \over 4}\left( {f\left( a \right) + f\left( b \right) + 2f\left( c \right)} \right).}

$\int\limits_0^{\pi /2} {\sin x\,dx = }$

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