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Example 6 | Pl Plane Ar eas in Rectang ular Coor dinates | Integ r al Calcul us Revi ew
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Example 6 | Plane Areas in Rectangular Coordinates Tags: vert vertica icall stri strip p are area a by in inte tegra grati tion on pl plane ane are areas as li lim mit its s of in integ tegrat ratio ion n up upw w ard pa parab rabol ola a cub cubic ic thi third rd deg degree ree curve points n ts of inte intersecti rsection on
Example 6 Find each of the two areas bounded by the curves y = x 3 - 4x and y = x2 + 2x. Solution Click here to show or hide the solution
→ upward parabola, vertex at (-1, -1), LR = 1
→ (approximate - for graphing purposes only) Maximum and minimum points of y = x 3 - 4x when x = 1.15, y = 1.153 - 4(1.15) = -3.08 when x = -1.15, y = (-1.15)3 - 4(-1.15) = 3.08 Maxima: Maxima: (-1.15, 3.08) Minima: (1.15, -3.08) Points of intersection:
when x = 0, y = 0 when x = 3, y = 3^3 - 4(3) = 15 when x = -2, y = (-2)^3 - 4(-2) y = 0 Points of intersection: (0, 0), (3, 15) and (-2, 0)
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