Consider the given statements Statement I: If f ( x ) is bounded for x [ a , b ] , then area bounded by curve y = f ( x ) , x-axis, x = a and x = b is ? a b f ( x ) ? d x Statement II: If f ( x ) is bounded and differentiable for x [ a , b ]

Question

Consider the given statements

Statement I: If $f (x)$ is bounded for $x \in [a, b]$ , then area bounded by curve $y = f (x)$ , x-axis, $x = a$ and $x = b$ is $\int_{a}^{b} f (x) d x$

Statement II: If $f (x)$ is bounded and differentiable for $x \in [a, b]$ , then the area between $y = f (x)$ and $y = f^{- 1} (x)$ is equal to double the value of $\int_{a}^{b}$ $| f (x) - x |$ $d x$

Smart Achievers · Accepted Answer

(4)

$Use definition of Area.$ $S_{1} (F),$ $S_{2} (F)$

Solution

1 Only Statement I is true

2 Only Statement II is true

3 Both Statement I and II are True

4 Both Statement I and II are false

Ans.
(4)

$Use definition of Area.$ $S_{1} (F),$ $S_{2} (F)$

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