Let y - gx be the inverse of a bijective mapping f-R- Rfx-3x3-2x The area bounded by graph of gx the x-axis and the ordinate at x - 5 is-

The correct option is D 13/4 From figure required area =∫ _ 0 ^ 1 ( 5 3 x ^ 3 2x ) dx =[ 5x 3 x ^ 4 / 4 2 x ^ 2 / 2 nbsp;] nbsp;_ 0 ^ ...

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Byju's Answer

Standard XII

Mathematics

Real Valued Functions

Let y = gx ...

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 graph of g(x) the 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 D $\frac{13}{4}$
From figure required area
$= \int_{0}^{1} (5 - 3 x^{3} - 2 x) d x$
$= {[5 x - \frac{3 x^{4}}{4} - \frac{2 x^{2}}{2}]}_{0}^{1}$
$= \frac{13}{4}$

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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

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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→Rf(x)=3x3+2x The area bounded by graph of g(x) the x-axis and the ordinate at x=5 is:

The correct option is D 134From figure required area=∫10(5−3x3−2x)dx =[5x−3x44−2x22]10 =134

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 graph of g(x) the x-axis and the ordinate at $x = 5$ is:

The correct option is D $\frac{13}{4}$
From figure required area
$= \int_{0}^{1} (5 - 3 x^{3} - 2 x) d x$
$= {[5 x - \frac{3 x^{4}}{4} - \frac{2 x^{2}}{2}]}_{0}^{1}$
$= \frac{13}{4}$