Question

Why cannot a curve crossing the \[x\]-axis within \[a,b\] be integrated directly from \[a\] to \[b\] to obtain total area?

Options

• The negative and positive areas will cancel each other out.

• The ordinates \[x=a\] and \[x=b\] do not exist.

• The curve must be an ellipse.

• Horizontal strips must always replace vertical strips.

Answer 1

A portion below the \[x\]-axis contributes a negative signed integral, while a portion above contributes a positive one. Direct integration can therefore cancel parts of the physical area.