The area (in sq. units) in the first quadrant bounded by the parabola, y=x²+1 , the tangent to it at the point (2,5) and the coordinate axes is :

Step-by-step solution

The equation of parabola x²=y-1 The equation of tangent at (2,5) to parabola is y-5= ( d y d x )_ (2,5) (x-2)y-5=4(x-2)4 x-y=3 Then, the required area = ₀² (x²+1 )-(4 x-3) d x- Area of A O D= ₀² (x²-4 x+4 ) d x- 1 2 3 4 3= [ (x-2)³ 3 ]₀²- 9 8 = 37 24