If the area bounded by the $x$-axis, the curve $y = f(x)$ and lines $x = a$ and $x = b$ is independent of $b,\ \forall\ b a$ ($a$ is a constant), then $f$ is

Question

If the area bounded by the $x$-axis, the curve $y = f(x)$ and lines $x = a$ and $x = b$ is independent of $b,\ \forall\ b > a$ ($a$ is a constant), then $f$ is

Dr. Abubacker · Accepted Answer

(a)
According to the given condition
$\int_{a}^{b}{f(x)dx = c}$
On differentiating $w.r.t.b$, we get
$f(b) = 0\  \Rightarrow \ f(x) = 0$

Q. If the area bounded by the $x$-axis, the curve $y = f(x)$ and lines $x = a$ and $x = b$ is independent of $b,\ \forall\ b > a$ ($a$ is a constant), then $f$ is

Explanation

Reviewed by Dr. Abubacker

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