Question

From the figure shown, A(x) is defined to be the area bounded by the x and y axes, the horizontal line y=3 and the vertical line at x. For example A(4)=12 is the area of the 4 by 3 rectangle.

(a) Evaluate A(2.5)

(b) Evaluate A(4) - A(1)​

Answer 1

$\textbf{Given:}$

$\textsf{A(x)=Area bounded by the x and y axes, the horizontal line y=3}$

$\textsf{and the vertical line at x}$

$\textbf{To find:}$

$\textsf{(a) A(2.5)}$

$\textsf{(b) A(4)-A(1)}$

$\textbf{Solution:}$

$\textsf{(a)}$

$\mathsf{A(2.5)}$

$\textsf{=Area of the 2.5 by 3 rectangle}$

$\mathsf{=2.5{\times}3}$

$\mathsf{=7.5}$

$\implies\boxed{\mathsf{A(2.5)=7.5}}$

$\mathsf{(b)}$

$\mathsf{A(4)-A(1)}$

$\mathsf{=(4{\times}3)-(1{\times}3)}$

$\mathsf{=12-3}$

$\mathsf{=9}$

$\implies\boxed{\mathsf{A(4)-A(1)=9}}$