Define a piecewise function h(x)= cases x , & 0 x 4, 4, & 4< x 6
MATHEMATICS · Multi-part · CBSE · Mathematics · Applications of Integrals · Applications of Integrals
Problem
Define a piecewise function
h(x)={x,4,0≤x≤4,4<x≤6,
and let k(x)=x−2 for 0≤x≤6. Region T consists of all points in the plane that lie between the graphs of h and k on the closed interval [0,6].
(a) Determine all x–values in [0,6] for which h(x)=k(x).
(b) For each subinterval determined by the x–values found in part (a), indicate which function lies above the other. Justify your answer with appropriate reasoning.
(c) Write an expression, involving one or more definite integrals, whose value equals the area of region T. Do not evaluate yet.
(d) Evaluate the integral expression from part (c) exactly, and then give a decimal approximation correct to the nearest tenth.