Question:

<b>Solution:</b><br/>(i) By using rectangle<br/>Area $OAED < \int_{0}^{1} e^{x^2} dx <$ Area $OABC$<br/>$1 < \int_{0}^{1} e^{x^2} dx < 1 \cdot e$<br/>$1 < \int_{0}^{1} e^{x^2} dx < e$<br/>(ii) By using triangle<br/>Area $OAED < \int_{0}^{1} e^{x^2} dx <$ Area $OAED +$ Area of triangle $DEB$<br/>$1 < \int_{0}^{1} e^{x^2} dx < 1 + \frac{1}{2} \cdot 1 \cdot (e - 1) \Rightarrow 1 < \int_{0}^{1} e^{x^2} dx < \frac{e + 1}{2}$