# How do you use the trapezoidal rule to approximate integral of #e^-3x^2 dx# between [0,1]?

Divide the domain

Approximate area:

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To use the trapezoidal rule to approximate the integral of ( e^{-3x^2} ) from ( x = 0 ) to ( x = 1 ), follow these steps:

- Divide the interval ([0, 1]) into ( n ) subintervals of equal width. Let's denote the width of each subinterval as ( \Delta x ).
- Compute the function values ( y_0, y_1, y_2, ..., y_n ) at the endpoints of each subinterval, where ( y_i = e^{-3x_i^2} ), and ( x_i ) represents the ( i )-th subinterval endpoint.
- Apply the trapezoidal rule formula to each subinterval: [ \text{Trapezoidal Rule} = \frac{\Delta x}{2} \left( y_0 + 2y_1 + 2y_2 + \cdots + 2y_{n-1} + y_n \right) ]
- Sum up the results from all subintervals to obtain the approximate value of the integral.

If you need further clarification on any step, feel free to ask.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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