Let y - g x be the inverse of a bijective mapping f - R - R - f x -3 x 3-2 x- The area bounded by the graph of g x - x-axis and the ordinate at x -5 isA- y-4 3B- 3-4C-D-

The correct option is C 7/4 f(x)= 3x^3 + 2x g(x)=f^ 1(x) ∫_0^5g(x)=∫_0^1f(x)= [ 3x^4/4+x^2 ]^1_0= [ 3/4+1 ]= 7/4 ...

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Byju's Answer

Standard XII

Mathematics

Graph of a^x 0<a<1

Let y = g x b...

Question

Let $y = g (x)$ be the inverse of a bijective mapping $f : R \to R, f (x) = 3 x^{3} + 2 x .$ The area bounded by the graph of $g (x),$ x-axis and the ordinate at $x = 5$ is

$\frac{5}{4}$

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$\frac{7}{4}$

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$\frac{9}{4}$

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$\frac{13}{4}$

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Solution

The correct option is B
$\frac{7}{4}$

$f (x) = 3 x^{3} + 2 x$

$g (x) = f^{- 1} (x)$

$\int_{0}^{5} g (x) = \int_{0}^{1} f (x) = {[\frac{3 x^{4}}{4} + x^{2}]}_{0}^{2} = [\frac{3}{4} + 1] = \frac{7}{4}$

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Similar questions

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On the basis of above information answer the following questions.

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Let y=g(x) be the inverse of a bijective mapping f:R→R, f(x)=3x3+2x. The area bounded by the graph of g(x), x-axis and the ordinate at x=5 is

The correct option is B 74 f(x)=3x3+2x g(x)=f−1(x) ∫50g(x)=∫10f(x)=[3x44+x2]10=[34+1]=74

Let $y = g (x)$ be the inverse of a bijective mapping $f : R \to R, f (x) = 3 x^{3} + 2 x .$ The area bounded by the graph of $g (x),$ x-axis and the ordinate at $x = 5$ is

The correct option is B
$\frac{7}{4}$

$f (x) = 3 x^{3} + 2 x$

$g (x) = f^{- 1} (x)$

$\int_{0}^{5} g (x) = \int_{0}^{1} f (x) = {[\frac{3 x^{4}}{4} + x^{2}]}_{0}^{2} = [\frac{3}{4} + 1] = \frac{7}{4}$