Solution As shown in the y 3x 2 meets x axis at x lies below x axis for xe x axis for xe 3 11 1 The required area Area of the region ACBA Area of the region ADEA 3x 2 dx 3 x Rationalised 2023 24 Fig 8 9 the line 2 and its graph 2 dx 3x 2 dx 1 2 1 4 and above Example 4 Find the area bounded by the curve y cos x between x 0 and x 2t 3n 0 Solution From the Fig 8 10 the required x area area of the region OABO area of the region BCDB area of region DEFD Thus we have the required area 2x cos xdx 1 cos x dx cos xdx cos xdx X sin x sin x sin x sin x APPLICATION OF INTEGRALS X CA 24 6 x 1 EIN B B 3 T 6 Fig 8 10 0 x 1 3x E republisted 1 2rt 297 F