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The area of the figure bounded by the pa...

The area of the figure bounded by the parabola `(y-2)^2=x-1,` the tangent to it at the point with the ordinate `x=3,` and the `x-a xi s` is `7s qdotu n i t e s` (b) `6s qdotu n i t e s` `9s qdotu n i t e s` (d) None of these

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The area enclosed between the curves y=(log)_e(x+e),x=(log)_e(1/y), and the x-axis is 2s qdotu n i t s (b) 1s qdotu n i t s 4s qdotu n i t s (d) none of these

The area bounded by the two branches of curve (y-x)^2=x^3 and the straight line x=1 is 1/5s qdotu n i t s (b) 3/5s qdotu n i t s 4/5s qdotu n i t s (d) 8/4s qdotu n i t s

The area bounded by the curve f(x)=x+sinx and its inverse function between the ordinates x=0a n dx=2pi is 4pis qdotu n i t s (b) 8pis qdotu n i t s 4s qdotu n i t s (d) 8s qdotu n i t s

The area bounded by the curve a^2y=x^2(x+a) and the x-axis is (a^2)/3s qdotu n i t s (b) (a^2)/4s qdotu n i t s (3a^2)/4s qdotu n i t s (d) (a^2)/(12)s qdotu n i t s

The area of the closed figure bounded by x=-1,x=2,a n d y={-x^2+2,xlt=1 2x-1,x >1a n dt h ea b s c i s s aa xi si s (16)/3s qdotu n i t s (b) (10)/3s qdotu n i t s (13)/3s qdotu n i t s (d) 7/3s qdotu n i t s

The area of the region enclosed between the curves x=y^2-1a n dx=|y|sqrt(1-y^2) is 1s qdotu n i t s (b) 4/3s qdotu n i t s 2/3s qdotu n i t s (d) 2s qdotu n i t s

The area of the triangle formed by the positive x- axis and the normal and tangent to the circle x^2+y^2=4 at (1,sqrt(3)) is (a)2sqrt(3)s qdotu n i t s (b) 3sqrt(2)s qdotu n i t s (c)sqrt(6)s qdotu n i t s (d) none of these

Let f(x)=x^3+3x+2a n dg(x) be the inverse of it. Then the area bounded by g(x) , the x-axis, and the ordinate at x=-2a n dx=6 is 1/4s qdotu n i t s (b) 4/3s qdotu n i t s 5/4s qdotu n i t s (d) 7/3s qdotu n i t s

Let f(x)=m in i mu m(x+1,sqrt(1-x)) for all xlt=1. Then the area bounded by y=f(x) and the x-axis is 7/3s qdotu n i t s 1/6s qdotu n i t s (11)/6s qdotu n i t s (d) 7/6s qdotu n i t s

The value of the parameter a such that the area bounded by y=a^2x^2+a x+1, coordinate axes, and the line x=1 attains its least value is equal to 1/4s qdotu n i t s (b) 1/2s qdotu n i t s 3/4s qdotu n i t s (d) -1s qdotu n i t s