If the area bounded by the x-axis- curve y-fx and the lines x-1- x-b is equal to -b2-1-2 for all b - 1- then fx is

The correct option is D x√(1+x^2) Atp, ∫_1^b f(x) dx = √(b^2+1) √(2) ∫_1^b f(x) dx = [√(x^2+1)]_1^b f(x) = d(√(x^2+1)) f(x) = x√(1+x^ ...

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Byju's Answer

Standard XII

Mathematics

Area between x=g(y) and y Axis

If the area b...

Question

If the area bounded by the x-axis, curve $y = f (x)$ and the lines $x = 1$ , $x = b$ is equal to $\sqrt{b^{2} + 1} - \sqrt{2}$ for all $b > 1$ , then $f (x)$ is

\sqrt{x - 1}

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\sqrt{x + 1}

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\sqrt{x^{2} + 1}

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\frac{x}{\sqrt{1 + x^{2}}}

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Solution

The correct option is D $\frac{x}{\sqrt{1 + x^{2}}}$
Atp,
$\int_{1}^{b} f (x) d x = \sqrt{b^{2} + 1} - \sqrt{2}$
$\int_{1}^{b} f (x) d x = [\sqrt{x^{2} + 1}]_{1}^{b}$
$f (x) = d (\sqrt{x^{2} + 1})$
$f (x) = \frac{x}{\sqrt{1 + x^{2}}}$

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If the area bounded by the x-axis, curve y=f(x) and the lines x=1, x=b is equal to √b2+1−√2 for all b>1, then f(x) is

The correct option is D x√1+x2Atp,∫b1f(x)dx=√b2+1−√2∫b1f(x)dx=[√x2+1]b1f(x)=d(√x2+1)f(x)=x√1+x2

If the area bounded by the x-axis, curve $y = f (x)$ and the lines $x = 1$ , $x = b$ is equal to $\sqrt{b^{2} + 1} - \sqrt{2}$ for all $b > 1$ , then $f (x)$ is

The correct option is D $\frac{x}{\sqrt{1 + x^{2}}}$
Atp,
$\int_{1}^{b} f (x) d x = \sqrt{b^{2} + 1} - \sqrt{2}$
$\int_{1}^{b} f (x) d x = [\sqrt{x^{2} + 1}]_{1}^{b}$
$f (x) = d (\sqrt{x^{2} + 1})$
$f (x) = \frac{x}{\sqrt{1 + x^{2}}}$