Sponsor Area

Application Of Integrals

Question
CBSEENMA12035717

Using integration, find the area of the region bounded by the triangle whose vertices are (-1, 2), (1, 5) and (3, 4).

Solution

Consider the vertices, A(-1, 2), B(1, 5) and C(3, 4).
Let us find the equation of the sides of the triangle increment ABC.
Thus, the equation of AB is:
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Now the area of increment ABC = Area of increment ADB + Area of increment BDC
therefore space Area space of space increment ADB space equals space integral subscript negative 1 end subscript superscript 1 open square brackets fraction numerator 3 straight x plus 7 over denominator 2 end fraction minus fraction numerator straight x plus 5 over denominator 2 end fraction close square brackets dx
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