Let `I=int_1^3sqrt(3+x^3)dx` , then the value of `I` will lie in the interval (a)`[4,6]` (b) `[1,3]` (c)`[4,2sqrt(30)]` (d) `[sqrt(15),sqrt(30)]`

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

Let I=int_1^2 (dx)/sqrt(2x^3-9x^2+12x+4) then

(1)/(sqrt(x+3)-sqrt(x-4))

int sqrt(x)(1+x^(1//3))^(4)dx " is equal to "

If f(x)="cos"(tan^(-1)x), then the value of the integral int_0^1xf^(x)dx"i s" (3-sqrt(2))/2 (b) (3+sqrt(2))/2 1 (d) 1-3/(2sqrt(2))

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

If the vertices of the parabola be at (-2,0) and (2,0) and one of the foci be at (-3,0) then which one of the following points does not lie on the hyperbola? (a) (-6, 2sqrt(10)) (b) (2sqrt6,5) (c) (4, sqrt(15)) (d) (6, 5sqrt2)

The length of the chord of the parabola y^2=x which is bisected at the point (2, 1) is (a) 2sqrt(3) (b) 4sqrt(3) (c) 3sqrt(2) (d) 2sqrt(5)

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

Evaluate int_(1)^(2)(sqrt(x)dx)/(sqrt(3-x)+sqrt(x)) .