Estimate the value of `int_(0)^(a)e^(x^(2))dx` using (i) rectangle, (ii) triangle.

Explanation

To estimate the value of the integral \( \int_{0}^{a} e^{x^2} \, dx \) using both rectangles and triangles, we will follow these steps:

### Step 1: Understand the Function
The function we are integrating is \( e^{x^2} \). This function is always positive and increases rapidly as \( x \) increases.

### Step 2: Draw the Graph
We will sketch the graph of \( y = e^{x^2} \) over the interval from \( 0 \) to \( a \). The graph starts at \( (0, 1) \) since \( e^{0^2} = e^0 = 1 \) and increases steeply as \( x \) increases.

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