Area Between Two Curves

In this topic:

(1) Proposition (Area Between Two Curves) If and are continuous with on the closed interval then the area between the two curves and is given by

(2) Example (Area Between Two Curves) Sketch the region bounded by and then find the area.

(3) Example (Area Between Two Curves) Sketch the region bounded by and then find the area.

(4) Example (Area Between Two Curves) Sketch the region bounded by and then find the area.

(5) Example (Area Between Two Curves) Sketch the region bounded by and then find the area between the two curves.

Proposition (Area Between Two Curves) If and are continuous with on the closed interval then the area between the two curves and is given by

Example (Area Between Two Curves) Sketch the region bounded by and then find the area between the two curves.

Solution. A sketch of the region is

area between two curves _gr_31.gif]

The points of intersection are and Notice that on and therefore the area between the curves is (using symmetry)

Example (Area Between Two Curves) Sketch the region bounded by and then find the area between the two curves.

Solution. A sketch of the region is

area between two curves _gr_46.gif]
The point of intersection is Notice that on and therefore the area between the curves is

Example (Area Between Two Curves) Sketch the region bounded by and then find the area between the two curves.

Solution. A sketch of the region is

area between two curves _gr_58.gif]

The point of intersection is found by solving So,

Thus the intersection points are and Notice that on and therefore the area between the curves is

Example (Area Between Two Curves) Sketch the region bounded by and then find the area between the two curves.

Solution. A sketch of the region is

area between two curves _gr_77.gif]

The point of intersection is found by solving So,

Thus the intersection points are and Notice that on and therefore the area between the curves is

Cite this as:
Area Between Two Curves
Published by Library of Math -- Online math organized by subject into topics.
Written by Smith, David A.
http://www.libraryofmath.com/area-between-two-curves.html