Question

calc help!!

Answer 1

@ybarrap help please!

Answer 2

Since the difference between each x datapoint is not uniform, we'll need to use this formula:
$$
\int_{a}^{b} f(x)\, dx \approx \frac{1}{2} \sum_{k=1}^{N} \left( x_{k+1} - x_{k} \right) \left( f(x_{k+1}) + f(x_{k}) \right)
$$
Fill in the following to apply this formulat:
$$
\begin{matrix}
x&f(x)&x_{k+1}-x_{k}&f(x_{k+1}+f_{k})&x_{k+1}-x_{k}\times f(x_{k+1}+f_{k})\\
1&4& & & \\
3&8&?&?&?\\
4&6&?&?&?\\
6&10&?&?&?\\
7&10&?&?&?\\
9&12&?&?&?\\
10&16&?&?&?\\
\end{matrix}
$$
Fill in all the \(?'s\) then sum that last column and divide by two to get your answer.

see - http://en.wikipedia.org/wiki/Trapezoidal_rule#Non-uniform_grid

Answer 3

wow im a little confused hahaha

Answer 4

Do you understand the formula?

Answer 5

i dont get what k would be

Answer 6

Oh Ok, so k is just the \(k^{th}\) \(x\) or \(f(x)\) value. For example, for \(k=1,k=2\), \(x_1=1,x_2=3\) and also \(f(x_1)=4,f(x_2)=8 \) and so on.

Does that make sense?

Answer 7

can we do the first upper left box? so i know what im doing? pleasee

Answer 8

Here is a corrected table (a few problems with indices and parenthesis):
$$
\begin{matrix}
x&f(x)&x_{k+1}-x_{k}&f(x_{k+1})+f(x_{k})&(x_{k+1}-x_{k})\times f(x_{k+1})+f(x_{k})\\
1&4& & & \\
3&8&?&?&?\\
4&6&?&?&?\\
6&10&?&?&?\\
7&10&?&?&?\\
9&12&?&?&?\\
10&16&?&?&?\\
\end{matrix}
$$

Answer 9

yes, go ahead and start