Advertisements
Advertisements
प्रश्न
\[\int\limits_0^1 \left\{ x \right\} dx,\] where {x} denotes the fractional part of x.
Advertisements
उत्तर
\[\text{We have}, \]
\[I = \int\limits_0^1 \left\{ x \right\} dx\]
\[\text{We know} \left\{ x \right\} = x, 0 < x < 1\]
\[ \therefore I = \int\limits_0^1 x\ dx\]
\[ = \left[ \frac{x^2}{2} \right]_0^1 \]
\[ = \frac{1}{2} - \frac{0}{2}\]
\[ = \frac{1}{2}\]
APPEARS IN
संबंधित प्रश्न
If \[\int\limits_0^a 3 x^2 dx = 8,\] write the value of a.
Write the coefficient a, b, c of which the value of the integral
\[\int\limits_0^\infty \frac{1}{1 + e^x} dx\] equals
\[\int\limits_0^\pi x \sin x \cos^4 x dx\]
\[\int\limits_2^3 e^{- x} dx\]
Evaluate the following using properties of definite integral:
`int_(-1)^1 log ((2 - x)/(2 + x)) "d"x`
If f(x) = `{{:(x^2"e"^(-2x)",", x ≥ 0),(0",", "otherwise"):}`, then evaluate `int_0^oo "f"(x) "d"x`
Choose the correct alternative:
Using the factorial representation of the gamma function, which of the following is the solution for the gamma function Γ(n) when n = 8 is
Choose the correct alternative:
If n > 0, then Γ(n) is
Evaluate the following:
`int ((x^2 + 2))/(x + 1) "d"x`
`int x^9/(4x^2 + 1)^6 "d"x` is equal to ______.
`int (x + 3)/(x + 4)^2 "e"^x "d"x` = ______.
The value of `int_2^3 x/(x^2 + 1)`dx is ______.
