`P rov et h a t4lt=int_1^3sqrt(3+x^2)lt=4sqrt(3)`

Prove that 4le int_(1)^(3) sqrt(3+x^(3)) dx le 2sqrt30 .

int(1)/(sqrt(3-4x))dx

int(1)/(sqrt(4x^(2)-4x+3))dx=

Evaluate : (i) int_(0)^(1)(3sqrt(x^(2))-4sqrt(x))/(sqrt(x))dx , (ii) int_(0)^(1)x cos(tan^(1)x)dx

int(1)/(sqrt(3-(x^(2))/(4)))

Prove that sin^(-1). ((x + sqrt(1 - x^(2))/(sqrt2)) = sin^(-1) x + (pi)/(4) , where - (1)/(sqrt2) lt x lt(1)/(sqrt2)

If x=cos t and y=sin t,p ro v et h a t(dy)/(dx)=(1)/(sqrt(3))att=(2 pi)/(3)

int_(1)^(2)(dx)/(sqrt(x^(2)+4x+3))

int(1)/(sqrt(4x+3))dx

Prove that ln 2 lt int_(0)^(1)(dx)/(sqrt(1+x^(4))) lt (pi)/2)