A) \[9\]
B) \[12\]
C) \[17\]
D) \[18\]
Correct Answer: C
Solution :
Let\[I=\int_{0}^{8}{|x-5|}\,\,dx\] \[=\int_{0}^{5}{(5-x)\,}dx+\int_{5}^{8}{(x-5)}\,dx\] \[=\left[ 5x-\frac{{{x}^{2}}}{2} \right]_{0}^{5}+\left[ \frac{{{x}^{2}}}{2}-5x \right]_{5}^{8}\] \[=25-\frac{25}{2}+\left[ \frac{64}{2}-40-\left( \frac{25}{2}-25 \right) \right]\] \[=\frac{25}{2}-8+\frac{25}{2}=17\] Alternative Solution: It is clear from [he figure that required area = area of\[\Delta OAD+\]area of\[\Delta ABC\] \[=\frac{1}{2}\times 5\times 5+\frac{1}{2}\times 3\times 3\] \[=\frac{34}{2}=17\]You need to login to perform this action.
You will be redirected in
3 sec