Areas Under Curves

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The area under the curve y = x from x = 0 to x = 2 is

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1. **Area Formula**: The area $A$ is the integral $\int_a^b y \, dx$.
2. **Setup Integral**: $\int_0^2 x \, dx$.
3. **Evaluate**:
   - $[\frac{x^2}{2}]_0^2 = \frac{2^2}{2} - \frac{0^2}{2}$
   - $= \frac{4}{2} = 2$.
4. **Geometric Check**: This area represents a right-angled triangle with base $2$ and height $2$. Area $= 1/2 	imes 2 	imes 2 = 2$.

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Areas Under Curves

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The area bounded by y = x² and y = x from x = 0 to x = 1 is

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