Question

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

Answer 1

$\begin{array}{l} A=\int_{a}^{b}|F(x)| d x =\int_{-7}^{11}|x-1| d x \\[1 em] \text { It is clear from The drawing that } \text { integration must be divided into } \text { two parts } \\[1 em] \begin{array}{l} A=\int_{-7}^{1}(-x+1) d x+\int_{1}^{11}(x-1) d x \\[1 em] =\left.\left(-\frac{x^{2}}{2}+x\right)\right|_{-7} ^{1}+\left.\left(\frac{x^{2}}{2}-x\right)\right|_{1} ^{11} \\[1 em] =\left(-\frac{1}{2}+1-\left(-\frac{49}{2}-7\right)\right)+\left(\frac{121}{2}-11-\left(\frac{1}{2}-1\right)\right) \\[1 em] =32+50 =82\\[1 em] \text { You can find The area of two } \text { tringles and add them } \\[1 em] \begin{array}{l} A=\frac{1}{2} \times 10 \times 10+\frac{1}{2} \times 8 \times 8 \\[1 em] =50+32 \\[1 em] =82 \end{array} \end{array} \end{array}$