Question

Among the given options, for what value of $dx$ will the area under the curve be most precise to the true value

• A.
  $dx=1$
• B.
  $dx=0.1$
• C.
  $dx=0.01$
• D.
  $dx=0.001$

Answer 1

The correct option is D

$dx=0.001$
The area under the curve is calculated by taking small rectangles as shown in the figure with length and breadth as function value and $dx$, where $dx$ is incremental length along $x$ axis.
So, more the number of these rectangles, smaller will be the loss in area.
Thus smaller value of $dx$ will ensure more precision in area under the curve.