Evaluate the integral to find the area between the curves: f(x)=x g(x)

dictetzqh

dictetzqh

Answered question

2021-12-05

Evaluate the integral to find the area between the curves:
f(x)=x
g(x)=x22x

Answer & Explanation

Todd Williams

Todd Williams

Beginner2021-12-06Added 18 answers

If p(x) and q(x) are continuous functions over an interval [m,n] and R is the region between the graphs of p(x) and q(x) and bounded dy the linex x-m and x-n respectively.,then the area of R is determined as
Area=mn|p(x)q(x)|dx.
Both the functions are polynomial functions and hence continuous.
Graph of the given functions:
image
Intersection points:(0,0),(3,3)
Area of between the curves =03|f(x)g(x)|dx
=03|x(x22x)|dx
=03xx2dx
=|x22x33|03
=[322333(022033)]
=|929|
=92=4.5 sq.units

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