Question

1. Find the area of the region bounded above by y = e^x, bounded below by y = x, and bounded on the sides

Answer 1

The area of the region bounded above by y= eˣ bounded by y = x, and bounded on the sides; x =0; and x = 1 is given as e¹ - 1.5.

What is the significance of "Area under the curve"?

This is the condition in which one process increases a quantity at a certain rate and another process decreases the same quantity at the same rate, and the "area" (actually the integral of the difference between those two rates integrated over a given period of time) is the accumulated effect of those two processes.

What is the justification for the above answer?

Area = $\int\limits^1_0 {(e^x-x)} \, dx$

= $\int\limits^1_0 {e^x-x} \, dx - \int\limits^1_0 {(x)} \, dx$

= e¹-(1/2-0); or

Area = e -1.5 Squared Unit

The related Graph is attached accordingly.

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