Advertisements
Advertisements
प्रश्न
Evaluate the following definite integrals as limit of sums `int_(-1)^1 e^x dx`
Advertisements
उत्तर


APPEARS IN
संबंधित प्रश्न
Evaluate the following definite integrals as limit of sums.
`int_a^b x dx`
Evaluate the following definite integrals as limit of sums.
`int_2^3 x^2 dx`
Evaluate the following definite integrals as limit of sums.
`int_1^4 (x^2 - x) dx`
Evaluate the definite integral:
`int_(pi/2)^pi e^x ((1-sinx)/(1-cos x)) dx`
Evaluate the definite integral:
`int_0^(pi/4) (sinx cos x)/(cos^4 x + sin^4 x)`dx
Evaluate the definite integral:
`int_0^1 dx/(sqrt(1+x) - sqrtx)`
Prove the following:
`int_0^1 xe^x dx = 1`
`int (cos 2x)/(sin x + cos x)^2dx` is equal to ______.
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`
if `int_0^k 1/(2+ 8x^2) dx = pi/16` then the value of k is ________.
(A) `1/2`
(B) `1/3`
(C) `1/4`
(D) `1/5`
\[\int\frac{1}{x} \left( \log x \right)^2 dx\]
\[\int\limits_0^1 \left( x e^x + \cos\frac{\pi x}{4} \right) dx\]
\[\int\frac{\sqrt{\tan x}}{\sin x \cos x} dx\]
Solve: (x2 – yx2) dy + (y2 + xy2) dx = 0
Evaluate `int_(-1)^2 (7x - 5)"d"x` as a limit of sums
If f and g are continuous functions in [0, 1] satisfying f(x) = f(a – x) and g(x) + g(a – x) = a, then `int_0^"a" "f"(x) * "g"(x)"d"x` is equal to ______.
Evaluate the following as limit of sum:
`int _0^2 (x^2 + 3) "d"x`
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_0^(1/2) ("d"x)/((1 + x^2)sqrt(1 - x^2))` (Hint: Let x = sin θ)
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
The limit of the function defined by `f(x) = {{:(|x|/x",", if x ≠ 0),(0",", "otherwisw"):}`
`lim_(x -> 0) (xroot(3)(z^2 - (z - x)^2))/(root(3)(8xz - 4x^2) + root(3)(8xz))^4` is equal to
Let f: (0,2)→R be defined as f(x) = `log_2(1 + tan((πx)/4))`. Then, `lim_(n→∞) 2/n(f(1/n) + f(2/n) + ... + f(1))` is equal to ______.
`lim_(n rightarrow ∞)1/2^n [1/sqrt(1 - 1/2^n) + 1/sqrt(1 - 2/2^n) + 1/sqrt(1 - 3/2^n) + ...... + 1/sqrt(1 - (2^n - 1)/2^n)]` is equal to ______.
