The table below gives selected values for the function f(x). Use a trapezoidal estimation, with 6 trapezoids to approximate the value of the integral from 1 to 2 of f of x, dx. Give 3 decimal places for your answer.

Question

anonymous · Answer

https://gyazo.com/0c664bbb486e2332ed456ba2ddaef650

anonymous · Answer

@terenzreignz Wanna see who can finish it first?

terenzreignz · Answer

I hate this kind of problem -_-

anonymous · Answer

Almost done anyways ;p

terenzreignz · Answer

OS was lagging on my end.
But sure, you can have this one :)

anonymous · Answer

I was gonna win either way

terenzreignz · Answer

How typically like you to challenge me to unfair games :D

anonymous · Answer

I got 19.6

terenzreignz · Answer

Is it 7.4?

terenzreignz · Answer

Oh. My bad :D

anonymous · Answer

Did you just guess?

terenzreignz · Answer

No. I calculated.

anonymous · Answer

How'd you get 7.4?

terenzreignz · Answer

Trapezoidal rule.
What's the correct answer?

anonymous · Answer

I don't know, I'm not given the answer.

anonymous · Answer

Leme cheat using my calculator skilz

anonymous · Answer

You were right

anonymous · Answer

God damn it

anonymous · Answer

roughly 7.36

anonymous · Answer

Either my method was wrong or I simply miscalculated.

terenzreignz · Answer

Maybe next time, you'll think twice before challenging me >:)

anonymous · Answer

I don't get how

terenzreignz · Answer

How did you know I was correct if you don't know how to do it?

anonymous · Answer

I did the same thing as always and still ending up with 19.6

terenzreignz · Answer

Why don't you show me what you did?

anonymous · Answer

My calculator

anonymous · Answer

Will a pic of my work do?

terenzreignz · Answer

sure.

anonymous · Answer

https://gyazo.com/b6b38482bd80bb2a7c46b00d994ba200

terenzreignz · Answer

Typos, galore.

It seems this is the summation you did:
$$\Large \sum_{n=1}^6 x_n\Delta f(x_n)$$

Whereas this is what you should have done:
$$\Large \sum_{n=1}^6 f(x_n)\Delta x_n$$

anonymous · Answer

Can you by any chance show me your work?

terenzreignz · Answer

No... it was done in my head :(
But let me try to expound

what you did was this $$\Large \left[\frac{\color{blue}{1+1.1}}{2}\right][\color{red}{3-1}]+\left[\frac{\color{blue}{1.1+1.3}}{2}\right][\color{red}{5-3}]...$$
When what you should have done was this: $$\Large \left[\frac{\color{red}{3+1}}{2}\right][\color{blue}{1.1-1}]+\left[\frac{\color{red}{5+3}}{2}\right][\color{blue }{1.3-1.1}]...$$

anonymous · Answer

Ok, got it.