Thanu dharshani. t. t Asked a Question
September 10, 2021 7:39 pmpts 30 pts
EXAMPLE 5 Find the area of the region between the x-axis and the graph of fx) = * -x*-2x, -1 sx<2. Area= y =x*- x-2x Solution First find the zeros of f. Since fx) = **-x-2x = xt*- x - 2) = xr + 1) 2). the zeros are x = 0, -1, and 2 (Fig. 4.24). The zeros partition [-1, 2] into two subintervals: [-1, 0], on which f>0 and [0, 2], on which f < 0. We integrate f over each subinterval and add the absolute values of the calculated values. -20 Integral over [-1,0}: 4.24 The region between the curve y=*-x-2x and the x-axis (Example 5). --- --20)dr -i Integral over [0, 2]: -0- Total enclosed area = -- Enclosed area:
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  • Navdeep
    0 to 2 integration -y.dx. because y is negative below axises
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  • Srj Best Answer
    because area is always positive. after calculating integral if that is negative we must have to take absolute value for area. please let me know if you have further doubts I will...
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