Question

using integration find the area of region bounded by the triangle whose vertices are (-1,0),(1,3)and(3,2).

Answer 1

Vertices of the triangle are A(-1, 2), B(1,5) and C(3,4)
Equation of the line segemnt AB is
y−25−2=x+11+1y252x111
⇒y−23=x+12y23x12 i.e., 2(y−2)=3(x+1)2y23x1
2y−4=3x+32y43x3
2y=3x+72y3x7
y=3x+72y3x72
Equation of the line segment BC is
y−54−5=x−13−1y545x131
y−5−1=x−12y51x12
y=5=−12y512(x−1)x1
y=−x+112yx112
Equation of the line segment CA is
y−42−4=x−3−1−3y424x313
⇒y−4−2=x−1−4⇒y−4=12y42x14y412(x−3)x3
y=x+52
it can be done like this

Answer 2

This is the detailed solution of your question.