Question

1. Find the area bounded by the curve y=| X-1 |, the x-axis and the lines x =-7 and x= 11

Answer 1

Having built the graphs, it is clearly visible that we need to find the sum of the areas of the spirit of the triangles, therefore the first triangle is the intersection of the graphs $y=-x+1 , x=-7, x-axis$ ; the second triangle, respectively $y=x-1, x=11, x-axis$ . The area of ​​the first triangle is$\int_a^b(-x+1)dx, a=-7, b=1 \rightarrow S_1=32$ . The area of ​​the second triangle is $\int_a^b(x-1)dx, a=1, b=11\rightarrow S_2=50.$ Thus, the area of ​​the figure limited by graphs equals $S_1 +S_2 =32+50=82$