Question

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

Answer 1

$\text{As shown in the figure},\\ \text{ the area is divided to parts}\\ A=\int\limits_{-7}^1(-x+1-0)dx+\int\limits_1^{11}(x-1-0)dx\\ =\int\limits_{-7}^1(-x+1)dx+\int\limits_1^{11}(x-1)dx\\ =(-x^2/2+x)|_{-7}^1+(x^2/2-x)|_1^{11}\\ =-0.5+1+49/2+7\\ +121/2-11-0.5+1\\ =82$