The area of the region bounded by the parabola (y – 2)2 = x – 1, the tangent to the parabola at the point (2, 3) and the x – axis is

Question

Arun · Answer

The equation of tangent at ( 2 , 3 ) is x − 2 y + 4 = 0 ∴ Required area is given by = ∫ 0 3 ​ [ ( y − 2 ) 2 + 1 − 2 y + 4 ] d y = ∫ 0 3 ​ [ ( y − 2 ) 2 − 2 y + 5 ] d y = ∫ 0 3 ​ [ ( y 2 − 6 y + 9 ) ] d y = [ 3 y 3 ​ − 3 y 2 + 9 y ] 0 3 ​ = [ 9 − 2 7 + 2 7 ] = 9 .

Vikas TU · Answer

Dear student Please refer the ssolved examples https://www.askiitians.com/iit-jee-integral-calculus/area-under-curves.aspx

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The area of the region bounded by the parabola (y – 2)2 = x – 1, the tangent to the parabola at the point (2, 3) and the x – axis is

The area of the region bounded by the parabola (y – 2)2 = x – 1, the tangent to the parabola at the point (2, 3) and the x – axis is

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The area of the region bounded by the parabola (y – 2)2 = x – 1, the tangent to the parabola at the point (2, 3) and the x – axis is

The area of the region bounded by the parabola (y – 2)2 = x – 1, the tangent to the parabola at the point (2, 3) and the x – axis is

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