Question

JCUre. 0.33 of 1 pt 3 of 40 (8 complete) HW Score: 1/08 5.2.29 Que Graph the following function. Then use geometry (not Riemann sums) to find the area and the net area of the region described The region between the graph of y x|-3 and the x-axis for -4sxs4 A) 10- 10- 10- 1C 10 10 -102 The area of the region is 10 (Type an integer or a simplified fraction) ss The net area of the region is 8(Type an integer or a simplitied fraction) More

Answer 1

The graph of function y=|x|-3 would be as shown below. Area of the region between the graph of y=|x|-3 and the x - axis for -4$\leq$ x $\leq$ 4 has been shaded in blue and black shades

4 2 1 3 -4 -5 -3 4 5 7 111 2 4 LC

The area shown in blue shade lies below the x axis and that shown in black shade lies above x- axis. The area in blue shade consists of a triangle with base length of 6 units from -3 to 3. The height of this triangle is 3 units from 0to -3. The area of this triangle would be= 1/2 base x height = 1/2 (6)(3)= 9 square units

The area shown in black shade consists of two triangles, each with base length of 1 unit and height also of 1 unit. The area of each of these triangles would be 1/2 (1)(1)= 1/2 sq unit. The area of the triangles together would be 1/2 +1/2 = 1 sq unit. Thus the total area of the region as stated would be= 9+1 = 10 sq units... Ans

For the nett area of this region, the portion lying below x-axis would be considered negative and that lying above x- axis would be considered positive. The nett area would thus be -9 +1 = - 8 sq units .... Ans

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