If the area of the region `{(x , y):0lt=ylt=x^2+1,0lt=ylt=x+1,0lt=xlt=2}` is `A` , then the value of `3A-17` is____

The area (in sq. units ) of the region A = { (x,y):(x - 1) [x] lt= y lt= 2 sqrtx , 0 lt= x lt= 2 ] where [t] denotes the greatest integer function is

Let f:[0, oo)->R be a continuous function such that f(x)=1-2x+int_0^x e^(x-t)f(t)dt for all x in [0, oo) . Then, which of the following statement(s) is (are) TRUE? The curve y=f(x) passes through the point (1, 2) (b) The curve y=f(x) passes through the point (2, -1) (c) The area of the region {(x , y) in [0, 1]xxR :f(x)lt=ylt=sqrt(1-x^2)} is (pi-2)/4 (d) The area of the region {(x , y) in [0, 1]xxR :f(x)lt=ylt=sqrt(1-x^2)} is (pi-1)/4

The area of the region for which o lt y lt 3 -2x -x^(2) and x gt 0 , is

If [] denotes the greatest integer less than or equal to the real number under consideration and -1lt=xlt0,0lt=ylt1,1lt=zlt2, the value of the determinant |{:([x]+1,[y],[z]),([x],[y]+1,[z]),([x],[y],[z]+1):}| is

If alpha, beta are the roots of x^(2) - 3x + a = 0 , a in R and lt 1 lt beta, then find the values of a

If tan x = 1, 0 lt x lt 90^(@) , then what is the value of 2 sin x cos x?

If (sin^(-1)x)^(2)-(cos^(-1)x)^(2)=a , 0 lt x lt 1 , a ne 0 , then the value of 2x^(2)-1 is

The equation of sinx+siny+sinz = - 3 for 0 lt= x lt= 2 pi, 0 lt= y lt= 2 pi, 0 lt=z lt= 2pi has :