(B) The area $A$ bounded by the curve $y = f(x)$,the $x$-axis,and the lines $x = a$ and $x = b$ is given by the integral $A = \int_{a}^{b} y \, dx$.He

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$\frac{15}{4} \text{ sq. units}$

(B) The area $A$ bounded by the curve $y = f(x)$,the $x$-axis,and the lines $x = a$ and $x = b$ is given by the integral $A = \int_{a}^{b} y \, dx$.Here,$y = x^3$,$a = 1$,and $b = 2$.Therefore,the area is:$A = \int_{1}^{2} x^3 \, dx$$A = \left[ \frac{x^4}{4} \right]_{1}^{2}$$A = \frac{1}{4} [2^4 - 1^4]$$A = \frac{1}{4} [16 - 1]$$A = \frac{15}{4} \text{ sq. units}$.Thus,the correct option is $(b)$.

Class 12 Mathematics Application of Integration Area bounded by region of single curve

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The area bounded by the curve $y = x^3$,the $x$-axis,and the two ordinates $x = 1$ and $x = 2$ is equal to:

A
$\frac{15}{2} \text{ sq. units}$
B
$\frac{15}{4} \text{ sq. units}$
C
$\frac{17}{2} \text{ sq. units}$
D
$\frac{17}{4} \text{ sq. units}$

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Application of Integration

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Area bounded by region of single curve

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The area bounded by the curve $y = x^3$,the $x$-axis,and the two ordinates $x = 1$ and $x = 2$ is equal to:

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