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Nilanjan Bhowmick AIR 3, CSIR NET (Earth Science)
Thanu Dharshani posted an Question
September 11, 2021 • 01:09 am
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30 points
30 points
- IIT JAM
- Mathematics (MA)
Why they took mod for region [0, 2]?????
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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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 add solution.
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Anonymous User
0 to 2 integration -y.dx. because y is negative below axises