Question

The area of the region bounded by the curve $y=x^3$, its tangent as $(1,1)$ and x-axis is

• A. $\frac{1}{12}$
• B. $\frac{1}{6}$
• C. $\frac{2}{17}$
• D. $\frac{2}{15}$

Answer 1

Answer: (A)

$\frac{1}{12}$

Equation of tangent at $A$ is $y=3x-2$.
Area of shaded region $={\int }_0^1{x}^{3}dx-{\int }_{2/3}^1(3x-2)dx=\frac{1}{4}-\frac{15}{18}+\frac{2}{3}=\frac{1}{12}$