Q. 8 - Calculus

Question

Shade in the regions between the two functions shown here on the intervals (a) [−2, 3]; (b) [−1, 2]; and (c) [1, 3]. Which of these regions has the largest area? The smallest? 

Step-by-Step Solution

Answer

Regions on the Interval  $\left[-2,3\right]$  has the largest area

Region on the interval  $[1, 3]$ has the smallest area

Step1. Given Information

The curve of two function is given  such that the two curve form the region between each other as follow :

Part (a) Step 1. Shade region between the curve on the interval - 2 , 3

Shade region between the curve on the interval $\left[-2,3\right]$ is as follow:

Part (b) Step 1. Shade region between the curve on the interval - 1 , 2

Shade region between the curve on the interval $\left[-1,2\right]$is as follow:

   

Part (c) Step 1. Shade region between the curve on the interval 1 , 3

 Shading the region between the curve on the interval $\left[1,3\right]$:

Step 2. Conclusion

From the figure above in all three part of the shaded region between the two curve on the interval $\left[-2,3\right], \left[-1,2\right] \&\left[1,3\right]$ respectively, It is clearly seen that

Regions on the Interval $\left[-2,3\right]$ has the largest area.

Region on the interval  $\left[1,3\right]$ has the smallest area.