The area bounded by the curves $y = f\left( x \right)$, the $x$-axis and the ordinates $x = 1$ and $x = b$ is $\left( {b - 1} \right)\sin \left( {3b + 4} \right)$. Then, $f\left( x \right)$ is

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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Application +4 | -1

The area bounded by the curves

y = f\left( x \right)

, the

x

-axis and the ordinates

x = 1

and

x = b

\left( {b - 1} \right)\sin \left( {3b + 4} \right)

. Then,

f\left( x \right)

View answer and explanation

Correct option: C

\sin \left( {3x + 4} \right) + 3\left( {x - 1} \right)\cos \left( {3x + 4} \right)

Option C (sin(3x + 4) + 3(x - 1)cos(3x + 4)) is correct because it is the derivative of the given area function, representing f(x).

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