The graph of a function consists of three line segments that connect the points to

MATHEMATICS · Multi-part · CBSE · Mathematics · Applications of Integrals · Applications of Integrals

Problem

The graph of a function hh consists of three line segments that connect the points (−4,0)(-4,0) to (0,3)(0,3), (0,3)(0,3) to (2,3)(2,3), and (2,3)(2,3) to (6,−1)(6,-1). (Assume straight-line segments between the listed points.) (a) Evaluate ∫−40h(x) dx\displaystyle \int_{-4}^{0} h(x)\,dx by interpreting the integral in terms of geometric area. (b) Evaluate ∫02h(x) dx\displaystyle \int_{0}^{2} h(x)\,dx in the same way. (c) Evaluate ∫26h(x) dx\displaystyle \int_{2}^{6} h(x)\,dx. (d) Hence determine ∫−46h(x) dx\displaystyle \int_{-4}^{6} h(x)\,dx and interpret the result in terms of net signed area.

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