Let `f (x)` be function defined on `[0,1] ` such that `f (1)=0` and for any `a in (0,1], int _(0)^(a) f (x) dx - int _(a)^(1) f (x) dx =2 f (a) +3a +b` where b is constant.
`int _(0)^(1) f (x) dx =`

Let f (x) be function defined on [0,1] such that f (1)=0 and for any a in (0,1], int _(0)^(a) f (x) dx - int _(a)^(1) f (x) dx =2 f (a) +3a +b where b is constant. b=

Let f (x) be function defined on [0,1] such that f (1)=0 and for any a in (0,1], int _(0)^(a) f (x) dx - int _(a)^(1) f (x) dx =2 f (a) +3a +b where b is constant. b=

Let f (x) be function defined on [0,1] such that f (1)=0 and for any a in (0,1], int _(0)^(a) f (x) dx - int _(a)^(1) f (x) dx =2 f (a) +3a +b where b is constant. The length of the subtangent of the curve y= f (x ) at x=1//2 is:

Let f (x) be function defined on [0,1] such that f (1)=0 and for any a in (0,1], int _(0)^(a) f (x) dx - int _(a)^(1) f (x) dx =2 f (a) +3a +b where b is constant. The length of the subtangent of the curve y= f (x ) at x=1//2 is:

int_(0)^(a)f(x)dx=int_(a)^(0)f(a-x)dx .

int _(0) ^(2a) f (x) dx = int _(0) ^(a) f (x) dx + int _(0)^(a) f (2a -x ) dx

If int_(-1)^(1)f(x)dx=0 then

If int_(-1)^(1)f(x)dx=0 then

Let f (x) be a conitnuous function defined on [0,a] such that f(a-x)=f(x)"for all" x in [ 0,a] . If int_(0)^(a//2) f(x) dx=alpha, then int _(0)^(a) f(x) dx is equal to

Let f (x) be a conitnuous function defined on [0,a] such that f(a-x)=f(x)"for all" x in [ 0,a] . If int_(0)^(a//2) f(x) dx=alpha, then int _(0)^(a) f(x) dx is equal to