Advertisements
Advertisements
प्रश्न
Evaluate the following definite integrals as limit of sums.
`int_0^4 (x + e^(2x)) dx`
उत्तर
APPEARS IN
संबंधित प्रश्न
Evaluate the following definite integrals as limit of sums.
`int_0^5 (x+1) dx`
Evaluate the definite integral:
`int_(pi/2)^pi e^x ((1-sinx)/(1-cos x)) dx`
Evaluate the definite integral:
`int_0^1 dx/(sqrt(1+x) - sqrtx)`
Prove the following:
`int_1^3 dx/(x^2(x +1)) = 2/3 + log 2/3`
Prove the following:
`int_(-1)^1 x^17 cos^4 xdx = 0`
Choose the correct answers The value of `int_0^1 tan^(-1) (2x -1)/(1+x - x^2)` dx is
(A) 1
(B) 0
(C) –1
(D) `pi/4`
Evaluate : `int_1^3 (x^2 + 3x + e^x) dx` as the limit of the sum.
Evaluate the following integral:
Evaluate the following integrals as limit of sums:
Evaluate `int_(-1)^2 (7x - 5)"d"x` as a limit of sums
Evaluate the following:
`int_0^2 ("d"x)/("e"^x + "e"^-x)`
Evaluate the following:
`int_0^(pi/2) (tan x)/(1 + "m"^2 tan^2x) "d"x`
Evaluate the following:
`int_(pi/3)^(pi/2) sqrt(1 + cosx)/(1 - cos x)^(5/2) "d"x`
The value of `int_(-pi)^pi sin^3x cos^2x "d"x` is ______.
The value of `lim_(x -> 0) [(d/(dx) int_0^(x^2) sec^2 xdx),(d/(dx) (x sin x))]` is equal to
Left `f(x) = {{:(1",", "if x is rational number"),(0",", "if x is irrational number"):}`. The value `fof (sqrt(3))` is
The limit of the function defined by `f(x) = {{:(|x|/x",", if x ≠ 0),(0",", "otherwisw"):}`
The value of `lim_(n→∞)1/n sum_(r = 0)^(2n-1) n^2/(n^2 + 4r^2)` is ______.
`lim_(n→∞){(1 + 1/n^2)^(2/n^2)(1 + 2^2/n^2)^(4/n^2)(1 + 3^2/n^2)^(6/n^2) ...(1 + n^2/n^2)^((2n)/n^2)}` is equal to ______.
