Mathematics

# Using definite integration, find area of the triangle with vertices at A(1,1),B(3,3)A(1,1),B(3,3).

##### SOLUTION
$e{q^n}\,of\,AB:$
$y - 1 = \frac{2}{2}\left( {x - 1} \right)$
$y - 1 = x - 1$
$y = x$
$e{q^n}\,of\,BC:$
$y - 3 = \frac{{ - 2}}{1}\left( {x - 3} \right)$
$y - 3 = - 2x + 6$
$2x + y = 9$
$Area = \int_1^3 {xdx} + \int_3^4 {\left( {9 - 2x} \right)dx} -\int\limits_1^4 1 dx$
$= \left( {\frac{{{x^2}}}{2}} \right)_1^3 + \left( {9x - {x^2}} \right)_3^4-3$
$= \frac{9}{2} - \frac{1}{2} + \left[ {\left( {36 - 16} \right) - \left( {27 - 9} \right)} \right]-3$
$= \dfrac{8}{2} + \left( {20 - 18} \right)-3$
$= 4+ 2-3$
$=3$. Its FREE, you're just one step away

Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
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