Q. 165.0( 2 Votes )

# Prove that the curves y^{2} = 4x and x^{2} = 4y divide the area of the square bounded by x = 0, y = 0, x = 4 and y = 4 into three equal parts. **[CBSE 2015, 2016]**

**[CBSE 2015, 2016]**

Answer :

Given; y^{2} = 4x and x^{2} = 4y

By solving

Area of the region bounded by the curve y=f(x), the x-axis and the ordinates x=a and x=b, where f(x) is a continuous function defined on [a,b], is given by .

Area of middle region

Area of lower region

Area of the upper region

= Area of Square − Area of middle region − Area of lower region

∴ The curves y^{2} = 4x and x^{2} = 4y divide the area of the square bounded by x = 0, y = 0, x = 4 and y = 4 into three equal parts

Rate this question :

Draw a rough sketch of the given curve y = 1 + |x +1|, x = –3, x = 3, y = 0 and find the area of the region bounded by them, using integration.

Mathematics - ExemplarCompute the area bounded by the lines x + 2y = 2, y – x = 1 and 2x + y = 7.

Mathematics - ExemplarUsing integration find the area of the region

}

Mathematics - Board PapersFind the area of the region {(x, y) : x^{2} + y^{2}≤ 4, x + y ≥ 2}.

Find the area of region bounded by the triangle whose vertices are (–1, 1), (0, 5) and (3, 2), using integration.

Mathematics - ExemplarEvaluate as limit of sums.

**OR**

Using integration, find the area of the following region:

Mathematics - Board Papers

The area of the region bounded by the y-axis, y = cos x and y = sin x, 0 ≤ x ≤ is.

Mathematics - ExemplarFind the area bounded by the lines y = 4x + 5, y = 5 – x and 4y = x + 5.

Mathematics - Exemplar