# 5

We know that the area between two curves is given by the (definite) integral of the height of the region defined by the two curves. To determine this region it is first necessary to find the point(s) where the two functions cross, i.e. , to find all solutions to the equation Here is one way to do this :

> y1 := 2 * x^3;

> y2 := -x^2 + 4*x + 3;

> solve( y1 = y2, x );

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To check these results and to get a picture of the region whose area we will find, plot the functions on an interval containing all of the points of intersection :

> plot( [ y1, y2 ], x=-2..2, title = `Plot for # 5` );

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The area of the region bounded by these two functions is

> area := Int( y2 - y1, x = -1 .. 3/2 );

> area = value( area );

> area = evalf( area );

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