Advertisements
Advertisements
Question
Integrate the following with respect to x :
`alpha beta x^(alpha - 1) "e"^(- beta x^alpha)`
Advertisements
Solution
`int alpha beta x^(alpha - 1) "e"^(- beta x^alpha)`
Put β xα = u
α β xα-1 dx = du
`int alpha beta x^(alpha - 1) "e"^(- beta x^alpha) * "d"x = int "e"^(- betax^alpha) (alpha beta) x^(alpha - 1) * "d"x`
= `int "e"^(- "u") * "du"`
= `("e"^(- "u"))/(- 1) + "c"`
`int alpha beta x^(alpha - 1) "e"^(- beta x^alpha) * "d"x = - "e"^(- beta x^alpha) + "c"`
APPEARS IN
RELATED QUESTIONS
Find the volume of the solid generated by the complete revolution of the ellipse `"x"^2/36 + "y"^2/25 = 1` about Y-axis.
Integrate the following functions with respect to x :
`[sqrt(x) + 1/sqrt(x)]^2`
Integrate the following functions with respect to x :
`(3 + 4cosx)/(sin^2x)`
Integrate the following functions with respect to x :
`1/((x - 1)(x + 2)^2`
Integrate the following functions with respect to x :
`x^3/((x - 1)(x - 2))`
Integrate the following with respect to x :
`(sin 2x)/("a"^2 + "b"^2 sin^2x)`
Integrate the following with respect to x :
`cosx/(cos(x - "a"))`
Integrate the following with respect to x:
27x2e3x
Integrate the following with respect to x:
`(x sin^-1 x)/sqrt(1 - x^2)`
Integrate the following with respect to x:
`sin^-1 ((2x)/(1 + x^2))`
Integrate the following with respect to x:
`"e"^(-x) cos 2x`
Find the integrals of the following:
`1/sqrt(9 + 8x - x^2)`
Integrate the following with respect to x:
`(x + 2)/sqrt(x^2 - 1)`
Integrate the following functions with respect to x:
`sqrt(x^2 + 2x + 10)`
Choose the correct alternative:
`int sqrt(tanx)/(sin2x) "d"x` is
Choose the correct alternative:
`int secx/sqrt(cos2x) "d"x` is
Choose the correct alternative:
`int tan^-1 sqrt((1 - cos 2x)/(1 + cos 2x)) "d"x` is
