Question

$If{\int }_2^{4}f\left(x\right)dx=\frac{1}{2}andf(6-x)=f\left(x\right),then{\int }_2^{4}xf\left(x\right)dx=$

• A. 3/4
• B. 1
• C. 3/2
• D. 2

Answer 1

The correct option is C

3/2

$I={\int }_2^{4}f\left(x\right)dx={\int }_2^4(6-x)f(6-x)dx={\int }_2^4(6-4)f(6-x)dx=6{\int }_2^{4}f\left(x\right)dx-{\int }_2^{4}xf\left(x\right)dx\therefore 2I=6\left(\frac{1}{2}\right)\Rightarrow I=\frac{3}{2}$