CBSE Class 12 · 2019 · Area Under CurvesLong Answer

Using method of integration, find the area of the triangle whose vertices are

(1, 0)

(2, 2)

and

(3, 1)

Answer: $\frac{3}{2}$ square units

Solution

Label

A (1, 0)

B (2, 2)

C (3, 1)

.
Equation of

A B

y = 2 x - 2

; equation of

B C

y = 4 - x

; equation of

A C

y = \frac{x - 1}{2}

Area = \int_{1}^{2} (2 x - 2) d x + \int_{2}^{3} (4 - x) d x - \int_{1}^{3} \frac{x - 1}{2} d x .

These give

1

\frac{3}{2}

and

1

respectively, so

A = 1 + \frac{3}{2} - 1 = \frac{3}{2}

.
Hence the area of the triangle is

\frac{3}{2}

square units.

CBSE Class 12 Board · 2019 · Subjective