Question

The following image shows the graph of the function $f\left(x\right)=\frac{1}{x}$ and three shaded rectangles.
What is the sum of the areas of the three rectangles pictured?

• A. 1.16
• B. 1.37
• C. 1.49
• D. 1.71
• E. none of these

Answer 1

The correct option is E none of these

Area of curve

$\Rightarrow$ ${\int }_1^4\frac{1}{x}dx=[lnx{]}_1^4$

$=2ln2$

Area of the rectangle

when $x=2,y=\frac{1}{x}=\frac{1}{2}$

$=1\times 1+[1\times \frac{1}{2}]+[1\times \frac{1}{3}]$

$\Rightarrow 1+\frac{1}{2}+\frac{1}{3}$

$\Rightarrow 1+0.5+0.33$

$\Rightarrow$ $1.833$