Question

What is the area of the region bounded by the line 3x - 5y = 15, x =1, x = 3 and x-axis in sq unit ?

• A. $\frac{36}{5}$
• B. $\frac{18}{5}$
• C. $\frac{9}{5}$
• D. $\frac{3}{5}$

Answer 1

Answer: (B)

$\frac{18}{5}$

Answer 2

The given equation of line can be rewritten as $\frac{x}{5} - \frac{y}{3} = 1$ and $y = \frac{3x-15}{5}$ $\therefore$ Required area $= \int^{3}_{1} ydx$ $= \int^{3}_{1} \left(\frac{3x-15}{5}\right)dx = \frac{1}{5} \int^{3}_{1} \left(3x-15\right)dx$ $= \frac{1}{5} \left[\frac{3x^{2}}{2} - 15x\right]^{3}_{1} = \frac{1}{5} \left[\frac{27}{2} - 45 - \frac{3}{2} + 15\right]$ $= \frac{1}{5} \left[\frac{24}{2} - 30\right] = \frac{1}{5}\left[12 - 30\right]$ $= \frac{-18}{5} = \frac{18}{5}$ sq unit (neglecting -ve sign)