The area of the region whose boundaries are defined by the curves y=`2cosx , y=`3tanx and the y-axis is (a) `1+31n(2/(sqrt(3)))s qdotu n i t s` (b)`1+3/2 1n3-31n2s qdotu n i t s` (c)`1+3/2 1n3-1n2s qdotu n i t s` (d)`1n3-1n2s 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 >1 and the ascissa axis is (a) (16)/3s qdotu n i t s (b) (10)/3s qdotu n i t s (c) (13)/3s qdotu n i t s (d) 7/3s 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 enclosed between the curve y^2(2a-x)=x^3 and the line x=2a above the x-axis is (a) pia^2s qdotu n i t s (b) (3pia^2)/2s qdotu n i t s (c) 2pia^2s qdotu n i t s (d) 3pia^2s 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

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 of the region bounded by x=0,y=0,x=2,y=2,ylt=e^x and ygeq1nx is (a) 6-41n2s qdotu n i t s (b) 41n2-2s qdotu n i t s 21n2-4s qdotu n i t s (d) 6-21n2s 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

The area bounded by the curves y=sinx between the ordinates x=0,\ x=pi and the x-axis is 2\ s qdotu n i t s b. 4\ s qdotu n i t s c. 3\ s qdotu n i t s d. 1\ s qdotu n i t s

The area of the region of the plane bounded by max(|x|,|y|)lt=1 and x ylt=1/2 is (a) 1/2+ln2 s qdot u n i t s (b) 3+ln2 s qdot u n i t s (c) (31)/4 s qdot u n i t s (d) 1+2ln2 s qdot u n i t s

The area bounded by the curves y=2x-2 , 2y+x=6 and x-axis (A) 5 squnits (B) 2s qdotu n t s (C) 4 s qdotu n t s (D) none of these