After working an integration problem for the area formed by two intersecting line functions (8-y) - (y-2)2/3 dy  between -4 and 5 in which I let u subsitition equal the (y-2)2/3 as follows: A = intergration from -4 to 5 (correctly checked) of (8-y) - ( u ) dy  gave an answer that was positive but did not match the book answer of 81/2.  My calculation for (dy ) was as follows:  du = (y2 - 4y + 4)/3  dy.  Since I am using this problem as a model to my understanding of Briggs Calculus chapter 6.2, 3rd ed., would you give me a step by step solution to this problem to help me understand the nature of my error(s)?

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.