Advertisements
Advertisements
Question
Evaluate the following:
`int_0^oo x^5 "e"^(-3x) "d"x`
Sum
Solution
We know that
`int_0^oo x^"n" "e"^(-"a"x) "d"x ("n"!)/("a"^("n" + 1))`
∴ `int_0^oo x^5 "e"^(-3x) "d"x = (5!)/(3^(5 + 1))`
= `(5!)/(3^6)` ......(Here n = 5, a = 3)
shaalaa.com
Gamma Integral
Is there an error in this question or solution?
Chapter 9: Applications of Integration - Exercise 9.7 [Page 122]
APPEARS IN
RELATED QUESTIONS
Evaluate the following:
`int_0^(pi/2) ("e"^(-tanx))/(cos^6x) "d"x`
Evaluate the following:
If `int_0^oo "e"^(-"a"x^2) x^3 "d"x` = 32, `alpha > 0`, find `alpha`
Choose the correct alternative:
The value of `int_0^1 x(1 - x)^99 "d"x` is
Choose the correct alternative:
If `("I'"("n" + 2))/("I'n")` = 90 then n is
Choose the correct alternative:
The value of `int_0^oo "e"^(-3x) x^2 "d"x` is
