If `int_0^1 e^(x^2)(x-alpha)dx=0`, then (a)`alphalt2` (b)= `alphalt0` `(c)="" 0ltalphalt1` (d)= `alpha="0`

int_(0)^(1)e^(2x)e^(e^(x) dx =)

Evaluate: int_0^1 e^(2-3x) dx

The value of the integral int_0^1(dx)/(x^2+2xcosalpha+1) is equal to (a) sinalpha (b) alphasinalpha (c) alpha/(2sinalpha) (d) alpha/2sinalpha

The value of int_0^(pi/2) sin|2x-alpha|dx, where alpha in [0,pi], is (a) 1-cos alpha (b) 1+cos alpha (c) 1 (d) cos alpha

If int_(0)^(oo) e^(-ax^(2)x^(3) dx = 32, alpha gt 0, find alpha .

The equation sin^4x+cos^4x+sin2x+alpha=0 is solvable for -5/2lt=alphalt=1/2 (b) -3lt=alpha<1 -3/2lt=alphalt=1/2 (d) -1lt=alphalt=1

Evaluate int_0^1(e^x)/(1+e^(2x)) dx

If sinx+cos e cx+tany+coty=4 where x and y in [0,pi/2] ,then tan(y/2) is a root of the equation (a) alpha^2+2alpha+1=0 (b) 2 alpha^2-2alpha-1=0 (c) 2alpha^2-2alpha-1=0 (d) alpha^2-alpha-1=0

If alphaa n dbeta are the roots of the equation x^2+b c+c=0 ,where cltaltb then a. 0ltalphaltbeta b. alphalt0ltbetalt|alpha| c. alphaltbetalt0 d. alphalt0lt |alpha|ltbeta