JEE Advanced questions
3844 published questions with worked solutions.
- _0^2 2+x 2-x ,dx is equal to
- The value of _0^ ^2x ,dx is
- If a_n= _0^ /2 ^2nx x ,dx then a_2-a_1, a_3-a_2, a_4-a_3, are in
- Let a_n= _0^ /4 ^nx ,dx. Then a_2+a_4, a_3+a_5, a_4+a_6 are in
- _1^ e^ 37 ( _ex) x ,dx is equal to
- Let d dx F(x)= e^ x x , x>0. If _1^4 2e^ x^2 x ,dx=F(k)-F(1) then one of the possible values of k is
- If f(x)= _ -1 ^ 1 x 1+t^2 ,dt then f' ! ( 3 ) is
- The value of _ ^3/27 ^ ^3/8 x ,dt, where t=x^3, is
- The value of _1^2[f g(x) ]^ -1 f' g(x) g'(x) ,dx, where g(1)=g(2), is equal to
- If f ! ( 1x )+x^2f(x)=0, x>0, and I= _ 1/x ^ x f(z) ,dz, 12 x 2, then I is
- _ /4 ^ 3 /4 dx 1+ x is equal to
- If f(x) satisfies the conditions of Rolle's theorem in [1,2] then _1^2f'(x) ,dx is equal to
- If f(x) be a quadratic polynomial such that f(0)=2, f'(0)=-3 and f''(0)=4 then _ -1 ^ 1 f(x) ,dx is equal to
- 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