`int_0^3 x(3-x)^(3/2) dx=` (A) `(108sqrt(3))/35` (B) `-(108sqrt(3))/35` (C) `(54sqrt(3))/35` (D) none of these

int_0^(4/pi) (3x^2sin(1/x)-xcos(1/x))dx= (A) (8sqrt(2))/pi^3 (B) (32sqrt(2))/pi^3 (C) (24sqrt(2))/pi^3 (D) sqrt(2048)/pi^3

int_(0)^(3)x sqrt(3-x)dx

int_(0)^(3)x sqrt(3-x)dx

The tangent to the graph of the function y=f(x) at the point with abscissae x=1, x=2, x=3 make angles pi/6,pi/3 and pi/4 respectively. The value of int_1^3f\'(x)f\'\'(x)dx+int_2^3f\'\'(x)dx is (A) (4-3sqrt(3))/3 (B) (4sqrt(3)-1)/(3sqrt(3)) (C) (4-3sqrt(3))/2 (D) (3sqrt(3)-1)/2

Given b=2,c=sqrt(3),/_A=30^(0), then inradius of o+ABC is (sqrt(3)-1)/(2) (b) (sqrt(3)+1)/(2) (c) (sqrt(3)-1)/(4) (d) none of these

If |cos^(-1)((1-x^(2))/(1+x^(2)))|<(pi)/(3), then x in[-(1)/(3),(1)/(sqrt(3))] (b) x in[-(1)/(sqrt(3)),(1)/(sqrt(3))]x in[0,(1)/(sqrt(3))](d) none of these

(sqrt(3)-(1)/(sqrt(3)))^(2) simplifies to (3)/(4)(b)(4)/(sqrt(3))(c)(4)/(3) (d) None of these

int_(0)^(3)sqrt((x)/(3-x))dx

int_(0)^(3)sqrt((3-x)/(x))dx

The value of lim_(x rarr2)(sqrt(1+sqrt(2+x))-sqrt(3))/(x-2) is (1)/(8sqrt(3))(b)(1)/(4sqrt(3)) (c) 0 (d) none of these