Mathematics : Application of Integrals

Find the area bounded by the curve  y = x² and the line y = x.
OR
Find the area of the region {(x. y): x² ≤ y ≤ x}.

Find the area of the region bounded by the line y = 3 x + 2, the x-axis and the ordinates x = - 1 and x = 1.

Find the area of the region enclosed by the parabola x² = y, the line y = x + 2 and the x-axis.
OR
Draw the rough sketch and find the area of the region:
{(x, y): x² < y < x + 2}

Draw a rough sketch of the curves y = sin x and y = cos x as x varies from 0 to  and find the area of the region enclosed by them and the x-axis.

Find the area bounded by the curve y = cos x between x = 0 and x = 2 .