CBSE Class 12 · 2006 · Area Under CurvesLong Answer

Find the area of the region bounded by

y^{2} = 4 x

x = 1

x = 4

and x-axis in the first quadrant.

Answer: $\frac{28}{3}$ square units

Solution

In the first quadrant the parabola gives

y = 2 x

. The region is bounded below by the

x

-axis and on the sides by

x = 1

and

x = 4

A = \int_{1}^{4} 2 x d x = 2 \cdot \frac{2}{3} x^{3/2}_{1}^{4} = \frac{4}{3} (8 - 1) = \frac{28}{3} .

Hence the required area is

\frac{28}{3}

square units.

CBSE Class 12 Board · 2006 · Subjective