Definite Integration questions
424 published questions with worked solutions.
- Let f:[0, ) [0, ) be defined as f(x)= _0^x[y]dy where [x] is the greatest integer less than or equal to x. Which of the following...
- If the value of the integral _0^5 x+[x] e^ x-[x] dx= e^ -1 + . where , R, 5 +6 =0, and [x] denotes the greatest integer less than...
- The value of _ n 1 n _ r=0 ^ 2n-1 n^2 n^2+4r^2 is
- For x > 0, if f(x)= _1^x _et (1+t) dt, then f(e)+f ( 1 e ) is equal to
- Let f(x)= _0^xe^tf(t)dt+e^x be a differentiable function for all x R. Then f(x) equals :
- If I_ m,n = _0^1x^ m-1 (1-x)^ n-1 dx, for m, n 1 and _0^1 x^ m-1 +x^ n-1 (1+x)^ m+n dx= I_ m,n , R, then equals________.
- The value of _ - /2 ^ /2 ^2x 1+3^x dx is
- The value of the integral _0^ | 2x|dx is
- The value of the integral _ - /2 ^ /2 dx (1 + e^x)( ^6x + ^6x) is equal to
- _ n ( n^2 (n^2+1)(n+1) + n^2 (n^2+4)(n+2) + n^2 (n^2+9)(n+3) + + n^2 (n^2+n^2)(n+n) ) is equal to
- _ n (1/2^ n )(1/ 1 - 1/2^ n + 1/ 1 - 2/2^ n + 1/ 1 - 3/2^ n + ... + 1/ 1 - (2^ n - 1)/2^ n ) is equal to
- For any real number x, let [x] denote the largest integer less than or equal to x. Let f be a real valued function defined on the...
- If _ n ((n + 1)^ k−1 /n^ k+1 )[(nk + 1) + (nk + 2) + ... + (nk + n)] = 33 _ n (1/n^ k+1 )[1^k + 2^k + 3^k + ... + n^k], then the...
- If b_ n = _ 0 ^ /2 ^ 2 nx/ x dx, n ℕ, then-
- _ 0 ^ 20 (| x| + |cos x|)^ 2 dx is equal to
- If a = _ n _ k=1 ^ n 2n/(n^ 2 + k^ 2 ) and f(x) = (1 − cos x)/(1 + cos x)), x (0, 1), then
- The value of the integral 48 ^4 _0^ ( 3 x^2 2 - x^3 ) x 1 + ^2x dx is equal to _____.
- The value of the integral _ - /4 ^ /4 x+ 4 2- 2x dx is :
- If _0^ 5^ x (1+ x 3x+ ^2x+ ^3x 3x) 1+5^ x dx= k 16 , then k is equal to __________.
- _ x [ 1 1+n + 1 2+n + 1 3+n + .+ 1 2n ] is equal to
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