Question

There are two curves in a graph. One is y = x² and the other is y = x. Find the area enclosed between these curves.
1. 1 / 6 unit
2. 1 / 16 unit
3. 1 unit
4. 1 / 2 unit

Answer 1

Correct Answer - Option 1 : 1 / 6 unit

Calculation:

Given:

y = x² 

y = x

Interconnection point,

x² = x

x = 1, y = 1

Area Enclosed (A) is given by, 

\(A=\mathop \smallint \limits_0^1 \left( {x - {x^2}} \right)dx\)

\(A = \left[ {\frac{{{x^2}}}{2} - \frac{{{x^3}}}{3}} \right]_0^1\)

\(A = \frac{1}{2} - \frac{1}{3}\)

\(A = \frac{1}{6}\) unit