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 ?
What is the area of the region bounded by the line 3x - 5y = 15, x =1, x = 3 and x-axis in sq unit ?
Updated On: Jul 7, 2022
- $\frac{36}{5}$
- $\frac{18}{5}$
- $\frac{9}{5}$
- $\frac{3}{5}$
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The Correct Option is B
Solution and Explanation
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)
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Applications of Integrals
There are distinct applications of integrals, out of which some are as follows:
In Maths
Integrals are used to find:
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In Physics
Integrals are used to find:
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