If `Delta(x)=|{:(a,b,c),(6,4,3),(x,x^(2),x^(3)):}|` then find `int_(0)^(1) Delta (x)`dx.

Let Delta(x)=|(x+a,x+b,x+a-c),(x+b,x+c,x-1),(x+c,x+d,x-b+d)| and int_0^2 Delta(x)dx=-16, where a,b,c,d are in A.P. then the common difference (i) 1 (ii) 2 (iii) 3 (iv) 4

Evaluate :- int_(0)^(1)(3x^(2)+4)dx

Evaluate : int_(0)^(4) x(4-x)^(3//2)dx

Find int_0^1(4x^3+3x^2-2x+1)dx

If Delta (x)=|{:(1,cos x,1-cos x),(1+sin x,cos x,1+sinx-cosx),(sinx,sinx,1):}| then int_(0)^(pi//2)Delta(x) dx is equal to

" If " Delta (x)=|underset(9" "x" "-7)underset(6" "4x" "3)(1" "x^(2)" "x^(2))| then find the value of overset(1)underset(0)(int)Delta (x) dx without expanding Delta (x) .

if Delta (x)= |{:(a_(1)+x,,b_(1)+x,,c_(1)+x),(a_(2)+x,,b_(2)+x,,c_(2)+x),(a_(3)+x,,b_(3)+x,,c_(3)+x):}| then show that Delta (x)=0 and that Delta (x)=Delta(0)+sx. where s denotes the sum of all the cofactors of all the elements in Delta (0)

If Delta_(1) = |(7,x,2),(-5,x +1,3),(4,x,7)| and Delta_(2) = |(x,2,7),(x +1,3,-5),(x,7,4)| , then the value of x for which Delta_(1) + Delta_(2) = 0 , is

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

Evaluate: int((x-x^3)^(1/3))/(x^4)dx