Answer :

Given; {(x, y): x^{2} ≤ y ≤ x}

By solving the equations y = x^{2} and y = x.

∴ x = 0,1

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 .

Required area

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