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(Solved): Find the area enclosed by the graphs of the functions y=2x3+3x2x and y=x2+3x. ...

$Find the area enclosed by the graphs of the functions \( y=2 x^{3}+3 x^{2}-x \) and \( y=x^{2}+3 x \).$

Find the area enclosed by the graphs of the functions

y = 2 x^{3} + 3 x^{2} ? x

and

y = x^{2} + 3 x

.

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Expert Answer

To find the area enclosed by the graphs of the given functions, we need to determine the points of intersection first. The area will be bounded by these intersection points

Setting the two functions equal to each other, we have:

2x^3 + 3x^2 - x = x^2 + 3x Rearranging the equation, we get: 2x^3 + 2x^2 - 4x = 0 Factoring out 2x, we have: 2x(x^2 + x - 2) = 0 Setting each factor equal to zero, we find:

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