7.5 Area Between Curvesap Calculus



Area between Curves

  1. 7.5 Area Between Curves Ap Calculus Calculator
  2. 7.5 Area Between Curves Ap Calculus Algebra

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.

7.5 Area Between Curvesap CalculusCurvesap

Area = (int_a^b {,left| {fleft( x right) - gleft( x right)} right|,dx} )

for a region bounded above by y = f(x) and below by y = g(x), and on the left and right by x = a and x = b.

for a region bounded on the left by x = f(y) and on the right by x = g(y), and above and below by y = c and y = d.

Example 1:1

Find the area between y = x and y = x2 from x = 0 to x = 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 x = y + 3 and x = y2 from y = –1 to y = 1.

(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