round answers to three decimal places. area of 1st rectangle =0.022 area of 2nd rectangle = area of 3rd…

Answer:

Area of 2nd rectangle = 0.0135 Area of 3rd rectangle = 0.007925 Area of 4th rectangle = 0.004375 Area of 5th rectangle = 0.0022 Area of 6th rectangle = 0.0011375 Total area = 0.0511375

Explanation:

Step1: Determine width of rectangles

The width of each rectangle is $\Delta x= 25$ (since the $x$-values increase by 25 each time: $700 - 675=25$).

Step2: Calculate area of 2nd rectangle

The height of the 2nd rectangle is $f(700) = 0.00054$. Area = height $\times$ width, so $A_2=0.00054\times25 = 0.0135$.

Step3: Calculate area of 3rd rectangle

The height of the 3rd rectangle is $f(725)=0.000317$. Area $A_3 = 0.000317\times25=0.007925$.

Step4: Calculate area of 4th rectangle

The height of the 4th rectangle is $f(750)=0.000175$. Area $A_4=0.000175\times25 = 0.004375$.

Step5: Calculate area of 5th rectangle

The height of the 5th rectangle is $f(775)=0.000091$. Area $A_5=0.000091\times25=0.002275\approx0.0022$.

Step6: Calculate area of 6th rectangle

The height of the 6th rectangle is $f(800)=0.000044$. Area $A_6=0.000044\times25 = 0.0011$.

Step7: Calculate total area

$A_{total}=0.022 + 0.0135+0.007925 + 0.004375+0.0022+0.0011 = 0.0511375$.