**Problem : **
Find the area of the region in the plane between the graphs of *f* (*x*) = | *x*| and
*g*(*x*) = - *x*^{2} + 6.

(- x^{2} + 6 - | x|)dx | = | (- x^{2} +6)dx - (- x)dx - xdx | |

= | + 6x - |_{-2}^{0} - |_{0}^{2} | ||

= |

**Problem : **
Find the total area between the graphs of *f* (*x*) = *e*^{x} and *g*(*x*) = 1 + 2*x* from *x* = - 1 to
*x* = 1.

| e^{x} - (1 + 2x)| dx | = | (e^{x} -1 - 2x)dx + (1 + 2x - e^{x})dx | |

= | [e^{x} - x - x^{2}]_{-1}^{0} + [x + x^{2} - e^{x}]_{0}^{1} | ||

= | 1 - + [(2 - e) - 1] | ||

= |

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