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Find the areas bounded by the indicated curves.$$y=x^{3}, y=x^{2}+4, x=-1$$

Calculus 2 / BC

Chapter 26

Applications of Integration

Section 2

Areas by Integration

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terrific. We want to find the area bounded by the two curves or rather three curves. Wife was x cubed. Wife was expert before and X equals negative one. This question is testing our knowledge of the application of integration known as the area between two curves. So we want to find the area between two curves. Given the formulas for vertical components. A integral A D v, y tu minus Y one D X or Y two Y one hour curves or horizontal components A equals integral C two D X two minus X one dy. So to solve this, what we need to do is sketch out are given curves, identify the relevant area and then identify what bounds and integration or rather integrations we need. So we get this out and see that the area is from negative 12 to the area between x squared plus four and execute that. We integrate on the X balance for expert plus four minus X cube. Best we've integral negative one or two extra performance X q b x is executed for three plus four, X minus X to the fourth or four evaluated. Maybe wanted to give the solution 45 divided by four.

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