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`

Let f(x)=x^3+3x+2 and g(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 (a) 9/2s qdotu n i t s (b) 4/3s qdotu n i t s (c) 5/4s qdotu n i t s (d) 7/3s qdotu n i t s

The area bounded by the curves y=sin^(-1)|sinx|a n dy=(sin^(-1)|sinx|^2,w h e r e0lt=xlt=2pi, is 1/3+(pi^2)/4 s qdotu n i t s (b) 1/6+(pi^3)/8s qdotu n i t s 2s qdotu n i t s (d) none of these

Area bounded by the curve x y^2=a^2(a-x) and the y-axis is (pia^2)/2s qdotu n i t s (b) pia^2s qdotu n i t s 3pia^2s 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 (a) 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

Consider two curves C_1: y^2=4[sqrt(y)]x a n dC_2: x^2=4[sqrt(x)]y , where [.] denotes the greatest integer function. Then the area of region enclosed by these two curves within the square formed by the lines x=1,y=1,x=4,y=4 is (a) 8/3s qdotu n i t s (b) (10)/3s qdotu n i t s (c) (11)/3s qdotu n i t s (d) (11)/4s qdotu n i t s

The area of the region containing the points (x , y) satisfying 4lt=x^2+y^2lt=2(|x|+|y|) is (a) 8s qdotu n i t s (b) 2s qdotu n i t s (c) 4pis qdotu n i t s (d) 2pis 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 bounded by the curves y=x e^x ,y=x e^(-x) and the line x=1 is 2/e s qdotu n i t s (b) 1-2/e s qdotu n i t s 1/e s qdotu n i t s (d) 1-1/e s qdotu n i t s

Area of the triangle formed by the line x+y=3 and angle bisectors of the pair of straight lines x^2-y^2+2y=1 is a. 2s qdotu n i t s b. 4s qdotu n i t s c. 6s qdotu n i t s d. 8s qdotu n i t s

The area bounded by the loop of the curve 4y^2=x^2(4-x^2) is (a)7/3 sq. units (b) 8/3s qdotu n i t e s (c)(11)/3s qdotu n i t s (d) (16)/3s qdotu n i t s