Solve the problem.
-The growth rate of a certain tree (in feet) is given by $y = \frac { 2 } { t + 1 } + e ^ { - t ^ { 2 } / 2 }$, where $t$ is time in years. Estimate the total growth of the tree through the end of the second year by using Simpson's rule. Use 2 subintervals. Round your answer to the nearest hundredth.
A) 3.68 ft
B) 3.41 ft
C) 5.11 ft
D) 2.34 ft

Question

Quizplus · Accepted Answer

Using Simpson's rule with 2 subintervals, we have:
$$\int_0^2 \frac{2}{t+1}+e^{-t^2/2}dt \approx \frac{2}{6} \left(\frac{2}{1+1}+e^{-0/2}+4\left(\frac{1}{1.5+1}+e^{-(1.5)^2/2}\right)+\frac{2}{3+1}+e^{-2^2/2}\right) \approx 3.41$$ Rounded to the nearest hundredth. Thus, the answer is B.

Solve the Problem y=2t+1+e−t2/2y = \frac { 2 } { t + 1 } + e ^ { - t ^ { 2 } / 2 }y=t+12​+e−t2/2

Solve the Problem $y = \frac { 2 } { t + 1 } + e ^ { - t ^ { 2 } / 2 }$