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# How large should $n$ be to guarantee that the Simpson's Rule approximation to $\displaystyle \int_0^1 e^{x^2}\ dx$ is accurate to within 0.00001?

## $n=20$

#### Topics

Integration Techniques

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### Video Transcript

problem. Plenty to have this problem. The only former we need to use this this one Arab on false Simpsons rule, right? A lot of fine K k the upper bond off the Farsi forest directive off. What is that? At this E to the expert. Let's start. He threw the X square. Uh, crying people, too, through acts times you to the Alps, where a crime crime is You go to to us for X square times of three. You go to eight acts. Thus, four acts this Hey, right, so for Oh, uh, they Oh, this is 12. So if you go to 12 plus, uh, 24 acts quick, just five times to 24 acts square, thus 16. That's the force e to the expert. Hi. Well, where's we actually flow? Toe his cuisine, Gerald one. So? So the maximum off the is. Well, thus before plus 24 plus 16. Time t right? Or a 60 76. Wow. Carries on McCain. So we want to used the formula here 76 e times. What money by I've been 80. But from there Okay into the force, right. Smaller, equal 10. So what to solve this The question why I did it for us? Greater than Oh, blast me. Let me use a calculator. Oh, there's no that one. It's quicker than a main point. Oh, I made a mistake. Okay? I made a mistake again. Maybe so. Any is greater than 19. But the others that in a skirt and 20 FBI aren't the hunger made a mistake, But it doesn't matter if you know how to compute. Ah, the era just used the only former one minute here, so it's okay.