Definite Integration questions
424 published questions with worked solutions.
- Consider the equation _1^e ( _e x)^ 1/2 x (a - ( _e x)^ 3/2 )^2 ,dx = 1, a (- , 0) (1, ). Which of the following statements...
- For positive integer n, define f(n) = n + 16 + 5n - 3n^2 4n + 3n^2 + 32 + n - 3n^2 8n + 3n^2 + 48 - 3n - 3n^2 12n + 3n^2 + + 25n...
- Let the function f: [1, ) R be defined by f(t) = cases (-1)^ n+1 ,2, & if t = 2n - 1, n N , [4pt] (2n + 1 - t) 2 f(2n - 1) + (t -...
- Let f be a differentiable function in (0, /2). If _ x ^ 1 t^ 2 f(t) dt = ^ 3 x + cos x, then (1/ 3 )f'(1/ 3 ) is equal to
- The value of the integral _ -2 ^ 2 |x^ 3 + x|/(e^ x|x| + 1) dx is equal to :
- Let I_ n (x) = _ 0 ^ x dt/(t^ 2 + 5)^ n , n = 1, 2, 3, ….. Then
- Let f : R R be a differentiable function such that f( /4) = 2 , f( /4) = 0 and f'( /2) = 1 and let g(x) = _ x ^ /4 (f'(t) sec t +...
- Let f : R R be a continuous function satisfying f(x) + f(x + k) = n, for all x R where k > 0 and n is a positive integer. If I_ 1...
- If f( ) = _ 1 ^ ( _ 10 t)/(1 + t) dt, > 0, then f(e^ 3 ) + f(e^ -3 ) is equal to :
- If _ 0 ^ 2 ( 2x - 2x - x^ 2 )dx = _ 0 ^ 1 (1 - 1 - y^ 2 - y^ 2 /2)dy + _ 1 ^ 2 (2 - y^ 2 /2)dy + I, then I equal is
- _ 0 ^ 5 ( (x − [x/2]))dx, where [t] denotes greatest integer less than or equal to t, is equal to :
- _0^ 2 | x- x| ,dx is equal to
- If = _ 1 2 ^ 2 ^ -1 x 2x^2 - 3x + 2 ,dx, then the value of 7 ( 2 7 ) is _____. (Here, the inverse trigonometric function ^ -1 x...
- Let f be a continuous function satisfying _0^ t^2 (f(x)+x^2)dx= 4 3 t^3, > 0. Then f ( ^2 4 ) is equal to -
- Let f be a differentiable function such that x^2f(x)-x=4 _0^xtf(t)dt, f(1) = 2 3 . Then 18 f(3) is equal to
- If f : R R be a continuous function satisfying _0^ /2 f( 2x) xdx+ _0^ /4 f( 2x) xdx=0, then the value of is
- If _ -0.15 ^ 0.15 |100x^2-1|dx= k 3000 , then k is equal to _________.
- Among (S1): _ n 1 n^2 (2+4+6+ +2n)=1 (S2): _ n 1 n^ 16 (1^ 15 +2^ 15 +3^ 15 + +n^ 15 )= 1 16
- If _0^1 1 (5+2x-2x^2)(1+e^ (2-4x) ) dx= 1 _e ( +1 ), , > 0, then ^4- ^4 is equal to-
- Let f be a differentiable function defined on [0, 2 ], such that f(x) > 0 and f(x) + _0^xf(t) 1-( _ef(t))^2 dt=e, [0, 2 ]. Then...
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