Question

Resolve the integral from 0 to 6 of xe^x with respect to x.

Answer 1

Answer:

$\int\limits^6_0 {xe^{x} } \, dx = 4e^5 +1$

Step-by-step explanation:

Step(i):-

Given

      $I = \int\limits^6_0 {xe^{x} } \, dx$

By using UV formula

$\int\limits {UV} \, dx = U\int\limits {v} \, dx - ( \int\limits {(U^{l} } \int\limits {v} \, dx \, )dx$

Now , we take  

     U = x and V = e ˣ

   U¹  = 1  and $\int\limits {e^{x} } \, dx = e^{x}$

Step(ii):-

$\int\limits {xe^x} \, dx = x\int\limits {e^x} \, dx - ( \int\limits {(1) } \int\limits {e^x} \, dx \, )dx$

           =  x e ˣ - $\int\limits {e^x} \, dx$

           = x e ˣ - e ˣ + C

$\int\limits^6_0 {xe^{x} } \, dx =( e^ x ( x -1) )_{0} ^{6}$

             = e⁵ (5-1) - (e⁰ (0-1)

             = 4 e⁵ + 1

Final answer:-

$\int\limits^6_0 {xe^{x} } \, dx = 4e^5 +1$