Definite Integration questions
424 published questions with worked solutions.
- Let (a,b) and ( , ) be two points on the curve y=f(x). If the slope of the tangent to the curve at (x,y) is (x), then _a^ (x) ,dx...
- If af(x)+bf ! ( 1x )= 1x-5, x 0, a b, then _1^2f(x) ,dx equals
- If f(x)= _ -1 ^ 1 x 1+t^2 ,dt then f' ! ( 3 ) is
- If f ! ( 1x )+x^2f(x)=0, x>0, and I= _ 1/x ^ x f(z) ,dz, 12 x 2, then I is
- Let I_n= _0^ /2 ^nx ,dx, n N. Then
- Let I_n= _0^ /4 ^nx ,dx, n N. Then
- _0^ /2 f(x) f(x) + f ! ( 2 - x ) ,dx, where f(x) -f ! ( 2 - x ) for 0 x 2 , has the value
- _0^a f(x) + f(-x) ,dx is equal to
- _ /5 ^ 3 /10 x x + x ,dx is equal to
- Let f(x) = x - [x] for x R , where [x] = the greatest integer x. Then _ -2 ^ 2 f(x) ,dx is
- _0^ ^6 x ^5 x ,dx is equal to
- _ -2 ^ 2 |1 - x^2| ,dx is
- _ - /4 ^ /4 e^x ^2 x ,dx e^ 2x - 1 is equal to
- _1^3 |(2 - x) _e x | dx is equal to
- _ -2 ^ 2 |x(x-1)| ,dx is
- The value of _ -2 ^ 2 ^2 x [ x ] + 12 ,dx, where [x] = the greatest integer greater than or equal to x, is
- If _0^x f(t) ,dt = x + _x^1 t f(t) ,dt then the value of f(1) is
- The value of _ -1 ^ 1 2 - x, 2, 1 + x is
- Let f be a positive function. If I_1 = _ 1-k ^ k x f x(1-x) ,dx, I_2 = _ 1-k ^ k f x(1-x) ,dx, where 2k - 1 > 0, then I_1 I_2 is
- If x (2n , 2n + ) then _0^x [ x] ,dx, where [x] = greatest integer less than or equal to x, is equal to
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