Question

approximate the integral with your calculator. round the answer to the nearest thousandth.\\(\int_{0}^{1} e^{x^3} \\, dx \approx ?\\)

Explanation:

Step1: Recall Integral of \( e^{x^3} \)

The function \( y = e^{x^3} \) does not have an elementary antiderivative, so we use numerical methods (e.g., calculator, Simpson's rule, or trapezoidal rule) to approximate \( \int_{0}^{1} e^{x^3} dx \).

Step2: Use Calculator for Approximation

Using a calculator (e.g., graphing calculator or software like Desmos, Wolfram Alpha) to compute the definite integral:

• Input the integral \( \int_{0}^{1} e^{x^3} dx \).
• The calculator will approximate the value. After calculation, we get approximately \( 1.201 \) (when rounded to the nearest thousandth).

Answer:

\( 1.201 \)