If - -ab fx dx - - -ab -fx- dx- a - b- then fx - 0 has

The correct option is C no root in (a, b) | ∫_a^b f(x) dx | ≤∫_a^b |f(x)| dx and the equality occurs only if the graph of y = f(x) lies entirely ab ...

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Byju's Answer

Standard XII

Mathematics

Graph of Functions x^(2n-1)

If | ∫ab fx...

Question

If $∣ ∣ ∣ \int_{a}^{b} f (x) d x ∣ ∣ ∣ = \int_{a}^{b} | f (x) | d x,$ a < b, then $f (x) = 0$ has

exactly one root in (a, b)

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at least one root in (a, b)

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no root in (a, b)

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none of these

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Solution

The correct option is C no root in (a, b)
$∣ ∣ ∣ \int_{a}^{b} f (x) d x ∣ ∣ ∣ \leq \int_{a}^{b} | f (x) | d x$
and the equality occurs only if the graph of $y = f (x)$ lies entirely above or below the x-axis for all x $\in$ (a, b).
Thus, $f (x) = 0$ has no real root in (a, b).

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If ∣∣∣∫baf(x)dx∣∣∣=∫ba|f(x)|dx, a < b, then f(x)=0 has

The correct option is C no root in (a, b)∣∣∣∫baf(x)dx∣∣∣≤∫ba|f(x)|dx and the equality occurs only if the graph of y=f(x) lies entirely above or below the x-axis for all x ∈ (a, b).Thus, f(x)=0 has no real root in (a, b).

If $∣ ∣ ∣ \int_{a}^{b} f (x) d x ∣ ∣ ∣ = \int_{a}^{b} | f (x) | d x,$ a < b, then $f (x) = 0$ has

The correct option is C no root in (a, b)
$∣ ∣ ∣ \int_{a}^{b} f (x) d x ∣ ∣ ∣ \leq \int_{a}^{b} | f (x) | d x$
and the equality occurs only if the graph of $y = f (x)$ lies entirely above or below the x-axis for all x $\in$ (a, b).
Thus, $f (x) = 0$ has no real root in (a, b).