Let `A=[underset(0" "1)overset(2" "q)""] and A^(8)=[underset(0" "1)overset(x" "yq)""],` then x-y is -

underset0overset2 int [x]dx =

Prove that : underset(0)overset(2a)intf(x) dx = underset(0)overset(2a)intf(2a-x)dx

underset0 overset1 int (dx)/(2x-3)

underset0overset8int x sqrt(x-4)dx

underset0overset1int(dx)/(2e^x-1)

underset0overset1int xlog(1+2x)dx

underset0 overset1 int (dx)/(1+x^2)

Let x_(1) lt x_(2) lt x_(3) lt x_(4) lt x_(5) and y_(1) lt y_(2) lt y_(3) lt y_(4) lt y_(5) are in AP such that underset(I = 1)overset(5)(sum) x_(i) = underset(I = 1)overset(5)(sum) y_(i) = 25 and underset(I =1)overset(5)(II) x_(i) = underset(I = 1)overset(5)(II) y_(i) = 0 then |y_(5) - x_(5)| A. 5//2 B. 5 C. 10 D. 15

Let x_(1) lt x_(2) lt x_(3) lt x_(4) lt x_(5) and y_(1) lt y_(2) lt y_(3) lt y_(4) lt y_(5) are in AP such that underset(I = 1)overset(5)(sum) x_(i) = underset(I = 1)overset(5)(sum) y_(i) = 25 and underset(I =1)overset(5)(II) x_(i) = underset(I = 1)overset(5)(II) y_(i) = 0 then |y_(5) - x_(5)|

underset(0)overset(pi)intxf(sin x)dx=A underset(0)overset(pi//2)int f(sin x) dx then A is