Question

Use the Trapezoidal Rule to approximate ∫0.8−1.2tanxx+9dx using n=3. Round your answer to the fourth decimal place.

Answer 1

Explanation

We are asked to simplify

$\int_{-1.2}^{0.8}\frac{tanx}{x+9}dx,\text{ n=3}$

To solve this, we will have

So that

$\Delta x=\frac{0.8-(-1.2)}{3}=\frac{2}{3}$

next, we will divide the intervals into 3

$\begin{gathered} We\text{ will divide \lbrack-1.2,0.8\rbrack into 3} \\ \end{gathered}$

$\begin{gathered} \text{ } \\ so\text{ we have} \\ -\frac{6}{5},-\frac{8}{15},\frac{2}{15},\frac{4}{5} \\ \end{gathered}$

Thus, we will have

So we will have

$-0.111597$

So the answer is -0.1116