" (a) "x sqrt(x+2)" I "

Evaluate the integerals. int (dx)/((2x +3) sqrt(x+2))on I sub (-2 , oo) \\{(-3)/(2)}.

Evaluate int (1)/(sqrt(sin ^(-1) x sqrt(1-x^(2))))dx on I= (0,1).

(i) int (dx)/(x sqrt(x^2-1)) (ii) int (dx)/(x sqrt(ax -x^2))

Evaluate: ( i )(x+1)/(sqrt(2x+3))dx (ii) int x sqrt(x+2)dx

Convert the following polar coordinates to its equivalent Cartesian coordinates. (i) ( i i ) (iii)2,pi)( i v ) (v) (ii) ( v i ) (vii)(( v i i i ) (ix)sqrt(( x )2( x i ))( x i i ) , (xiii)pi/( x i v )6( x v ) (xvi) (xvii))( x v i i i ) (xix) (iii) ( x x ) (xxi)(( x x i i ) (xxiii)-3,-( x x i v )pi/( x x v )6( x x v i ) (xxvii) (xxviii))( x x i x ) (xxx)

Factorise: (i) 4sqrt(3)x^(2) + 5x-2sqrt(3) (ii) 7sqrt(2)x^(2)-10x - 4sqrt(2)

The value of ("lim")_(xvec2)(sqrt(1+sqrt(2+x))-sqrt(3))/(x-2)i s (a) 1/(8sqrt(3)) (b) 1/(4sqrt(3)) (c) 0 (d) none of these

The value of ("lim")_(xto2)(sqrt(1+sqrt(2+x))-sqrt(3))/(x-2)i s (a) 1/(8sqrt(3)) (b) 1/(4sqrt(3)) (c) 0 (d) none of these

Evaluate int (1)/(sqrt( sin^(-1)x) sqrt(1-x^(2))) dx " on " I=(0,1)