# How do you use the trapezoidal rule with n=5 to approximate the area between the curve y=(3x^2+4x+2) from 0 to 3?

Aug 29, 2015

$49.296$ square units

#### Explanation:

First, compute the length of your interval $= \frac{3 - 0}{5} = 0.6$ units

Second, determine the $x$-values you need to use to compute $y$ (i.e. $x = 0.6 , 1.2 , 1.8 , 2.4 , 3.0$)

Third, compute $y$ using these $x$-values: $y = 5.48 , 11.12 , 18.92 , 28.88 , 41.00$ respectively

Fourth, use the trapezoidal rule:

$A = \frac{1}{2} \left(0.6\right) \left[5.48 + 2 \left(11.12\right) + 2 \left(18.92\right) + 2 \left(28.88\right) + 41.00\right] = 49.296$ square units