Prove that: `4leint_1^3sqrt(3+x^3)dxle2sqrt(30)`

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

Prove that 4<=int_(1)^(3)sqrt(3+x^(2))<=4sqrt(3)

Prove that pi/6leint_0^1dx/sqrt(4-x^2-x^3)lepi/(4sqrt(2))

Prove that : [tan^(-1) (-sqrt(3))] = -2/sqrt(3)

Prove that the lines sqrt(3)x+y=0,sqrt(3)y+x=0,sqrt(3)x+y=1 and sqrt(3)y+x=1 form a rhombus.

Prove that (2sqrt(3)+3)sin x+2sqrt(3)cos x lies between -(2sqrt(3)+sqrt(15)) and (2sqrt(3)+sqrt(15))

Prove that: (sqrt(3x5^(-3))-:3^(-1)3sqrt(5))x3x5^(6)6=(3)/(5)

Prove that (i) (1)/(3+sqrt(7)) + (1)/(sqrt(7)+sqrt(5))+(1)/(sqrt(5)+sqrt(3)) +(1)/(sqrt(3)+1)=1 (ii) (1)/(1+sqrt(2))+(1)/(sqrt(2)+sqrt(3))+(1)/(sqrt(3)+sqrt(4))+(1)/(sqrt(4)+sqrt(5))+(1)/(sqrt(5)+sqrt(6))+(1)/(sqrt(6)+sqrt(7)) +(1)/(sqrt(7)+sqrt(8))+(1)/(sqrt(8) + sqrt(9)) = 2

Prove that ((i-sqrt(3))/(-i+sqrt(3)))^(200)+((i-sqrt(3))/(i+sqrt(3)))^(200)=-1