(Solved): Lower Sum Midpoint Sum The applet above displays the graph of the function \( f(x)=x^{2} \). The g ...

Lower Sum Midpoint Sum The applet above displays the graph of the function \( f(x)=x^{2} \). The goal is to estimate the area bounded by the curve \( f \), line \( x=1, x=2 \) and the \( x \)-axis. a. Select the box "Upper Sum". You will see four blue rectangles. i. What is the width of each rectangle? Give the exact answer for all questions below. ii. What is the height of the left-most rectangle? iii. What is the height of the second to the left rectangle? iv. What is the height of the second to the right rectangle? v. What is the height of the right-most rectangle? vi. Use the information from \( i-v \) to find the total area of the four blue rectangles. Compare your answer with the number on the applet. Is the answer an overestimate or an underestimate? b. Uncheck the box "Upper Sum" and select the box "Lower Sum". You will see four yellow rectangles. Note that these rectangles have the same width as those in part a. i. What is the height of the left-most rectangle? ii. What is the height of the right-most rectangle? iii. Explain how the heights of yellow rectangles are being chosen and find the total area of the four yellow rectangles. Compare your answer with the number on the applet. Is the answer an overestimate or an underestimate? c. Uncheck the box "Lower Sum" and select the box "Midpoint Sum". You will see four green rectangles. Note that these rectangles have the same width as those in part a. Compare the total area of the four green rectangles with the total area in part a and b. Is the answer an overestimate or anderestimate? d. Which sum is the best estimate the area bounded by the curve \( f \), line \( x=1, x=2 \) and the \( x \)-axis?