Advertisements
Advertisements
प्रश्न
विकल्प
π/4
π/2
π
1
उत्तर
1
\[\text{We have}, \]
\[ I = \int_0^\frac{\pi}{2} x \sin x\ d x \]
\[ = \left[ - x \cos x \right]_0^\frac{\pi}{2} - \int_0^\frac{\pi}{2} 1\left( - \cos x \right) d x\]
\[ = \left[ - x \cos x \right]_0^\frac{\pi}{2} + \int_0^\frac{\pi}{2} \cos x\ d x\]
\[ = - \left[ x \cos x \right]_0^\frac{\pi}{2} + \left[ \sin x \right]_0^\frac{\pi}{2} \]
\[ = - \left[ 0 - 0 \right] + \left[ 1 - 0 \right]\]
\[ = 1\]
APPEARS IN
संबंधित प्रश्न
Evaluate each of the following integral:
\[\int\limits_0^\pi \frac{1}{1 + \sin x} dx\] equals
The value of \[\int\limits_0^{2\pi} \sqrt{1 + \sin\frac{x}{2}}dx\] is
The derivative of \[f\left( x \right) = \int\limits_{x^2}^{x^3} \frac{1}{\log_e t} dt, \left( x > 0 \right),\] is
\[\int\limits_0^{\pi/2} \frac{\sin^2 x}{\left( 1 + \cos x \right)^2} dx\]
\[\int\limits_0^{\pi/2} \frac{\sin x}{\sqrt{1 + \cos x}} dx\]
\[\int\limits_0^{\pi/4} \cos^4 x \sin^3 x dx\]
\[\int\limits_1^3 \left| x^2 - 2x \right| dx\]
\[\int\limits_0^1 \left| \sin 2\pi x \right| dx\]
\[\int\limits_0^{15} \left[ x^2 \right] dx\]
Evaluate the following:
f(x) = `{{:("c"x",", 0 < x < 1),(0",", "otherwise"):}` Find 'c" if `int_0^1 "f"(x) "d"x` = 2
Evaluate the following:
Γ(4)
Evaluate the following:
`int_0^oo "e"^(-4x) x^4 "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:
`Γ(3/2)`
Choose the correct alternative:
`int_0^oo x^4"e"^-x "d"x` is
If x = `int_0^y "dt"/sqrt(1 + 9"t"^2)` and `("d"^2y)/("d"x^2)` = ay, then a equal to ______.
`int x^3/(x + 1)` is equal to ______.
If `intx^3/sqrt(1 + x^2) "d"x = "a"(1 + x^2)^(3/2) + "b"sqrt(1 + x^2) + "C"`, then ______.
