HARD
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Let fx be a positive differentiable function on 0, a such that f0=1 and fa=314 if f'xfx3+fx-1, then, maximum value of a is

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Important Questions on Definite Integration

MEDIUM
The value of -π2π2x2cosx1+ex dx is equal to
MEDIUM
The value of the integral -ππcos2x1+axdx, a>0 is
EASY
03xdx=______, where x is greatest integer function
HARD
Let f:RR be a function such that f2-x=f2+x and f4-x=f4+x, for all xR and 02fxdx=5. Then the value of 1050fxdx is
MEDIUM
If 0π2 logcosx dx=π2log12, then 0π2 logsecx dx=
HARD
Let x>0 be a fixed real number. Then the integral 0e-1x-tdt is equal to-
HARD
The integral 0π1+sin2x2-sinx2dx equals 
HARD
Let fx=max3, x2,1x2 for 12x2. Then the value of the integral 122fxdx is
EASY
If 1 4 f( x )dx=4 and 2 4 ( 3f( x ) )dx=7 , then 1 2 f( x )dx is
EASY
Let f and g be continuous functions on 0,a such that fx=fa-x and gx+ga-x=4, then 0afxgxdx is equal to
HARD
For a real number x, let x denote the largest integer less than or equal to x and x=x-x. Let n be a positive integer. Then 0ncos 2πxxdx is equal to
HARD
The integral value of  0 π 2 2 sinx 2 sinx + 2 cosx dx=
HARD
If px is a cubic polynomial with p1=3, p0=2 and p-1=4, then -11pxdx is-
HARD
For real x with -10x10 define fx=-10x2tdt , where for a real number r we denote by r the largest integer less than or equal to r . The numbers of points of discontinuity of f in the interval -10, 10 is
HARD
Define a function f :RR by fx=maxx, x-1,.,x-2n, where n is a fixed natural number. Then 02nfxdx is-
HARD
Define gx=-33fx-yfydy, for all real x, where ft=1,0t10,elsewhere, then
MEDIUM

Statement - I : The value of the integral π/6π/3dx1+tan x is equal to π6.

Statement - II : abfxdx=abfa+b-xdx.

MEDIUM
The integral 24logx2logx2+log6-x2dx is equal to