" (1) "(1)/(9)x^(2)-(2)/(3)x=-1

(1) / (3) x ^ (2) -2x-9

(x-3)/(9)-(x-2)/(10)=1

If cos^(-1)(6x)/(1+9x^(2))=-(pi)/(2)+tan^(-1)3x, then find the value of x.

For x in(0,1) arrange f_(1)(x) = (1)/(9-x^(2)), f_(2)(x) = (1)/(9-2x^(2)) and f_(3)(x) = (1)/(9-x^(2)-x^(3)) in ascending order and hence prove that 1/6 ln2 lt int_(0)^(1)(1)/(9-x^(2)-x^(3)) dx lt (1)/(6sqrt(2)) ln 5 .

For x in(0,1) arrange f_(1)(x) = (1)/(9-x^(2)), f_(2)(x) = (1)/(9-2x^(2)) and f_(3)(x) = (1)/(9-x^(2)-x^(3)) in ascending order and hence prove that 1/6 ln2 lt int_(0)^(1)(1)/(9-x^(2)-x^(3)) dx lt (1)/(6sqrt(2)) ln 5 .

If x^(2)+(1)/(x^(2))=(82)/(9), Then find the value of x^(3)-(1)/(x^(3))

The term independent of x in the expression of (1+x+2x^(3))((3)/(2)x^(2)-(1)/(3x))^(9) is:

If int(sqrt(1-x^(2)))/(x^(4))dx=A(x)*(sqrt(1-x^(2)))^(m) where A(x) is a function of x then (A(x))^(m)= (A) -(1)/(27x^(9))(B)(1)/((27x)^(9))(C)(1)/(3x^(9))(D)-(1)/(3x^(9))

int_(-1)^(1) (1+x^(3))/(9-x^(2)) dx =

int_(-1)^(1) (1+x^(3))/(9-x^(2)) dx =