Area between Curves
Be able to nd the area between the graphs of two functions over an interval of interest. Know how to nd the area enclosed by two graphs which intersect. PRACTICE PROBLEMS: 1. Let Rbe the shaded region shown below. (a) Set up but do not evaluate an integral (or integrals) in terms of xthat represent(s) the area of R. AP Calculus: Area Between Two Curves Name: Sketch the graph of each equation, and then use your sketch to set up the integral to find the area between the curves. Use a calculator to evaluate your integral. ( )= 2+2, =−, =−2,and =1 2. ( )=6− 2and ( )= 3.
The area between curves is given by the formulas below.
Area = (int_a^b {,left| {fleft( x right) - gleft( x right)} right|,dx} ) | |
for a region bounded above by | |
for a region bounded on the left by | |
Example 1:1 | |
(eqalign{{rm{Area}} &= int_0^1 {left| {x - {x^2}} right|dx} &= int_0^1 {left( {x - {x^2}} right)dx} &= left. {left( {frac{1}{2}{x^2} - frac{1}{3}{x^3}} right)} right|_0^1 &= left( {frac{1}{2} - frac{1}{3}} right) - left( {0 - 0} right) &= frac{1}{6}}) | |
1 | Find the area between |
(eqalign{{rm{Area}} &= int_{ - 1}^1 {left| {y + 3 - {y^2}} right|dy} &= int_{ - 1}^1 {left( {y + 3 - {y^2}} right)dy} &= left. {left( {frac{1}{2}{y^2} + 3y - frac{1}{3}{x^3}} right)} right|_{ - 1}^1 &= left( {frac{1}{2} + 3 - frac{1}{3}} right) - left( {frac{1}{2} - 3 + frac{1}{3}} right) &= frac{{16}}{3}}) |
7.5 Area Between Curves Ap Calculus Calculator
See also
7.5 Area Between Curves Ap Calculus Algebra
Area under a curve, definite integral, absolute value rules