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Integrate the following with respect to x: -3 ∫ 3 (5x 4 /1+e -x )dx =

Integrate the following with respect to x:
-3∫3(5x4/1+e-x)dx =

Grade:10

2 Answers

Aditya Gupta
2081 Points
2 years ago
hello meenu, let J= -3∫3(5x4/1+e-x)dx …..(1)
now, we know by properties of definite integral that we can replace the fn f(x) inside by f(a+b – x) or f( – 3+3 – x)= f( – x)
so, J= -3∫3(5( – x)4/1+ex)dx
or J= -3∫3(5x4/1+ex)dx ….....(2)
now, write (1) as J= -3∫3(5ex.x4/1+ex)dx …......(3)
add (2) and (3)
2J= -3∫3(5x4/1+ex)*(1+ex)dx = -3∫35x4dx = x^5| – 3 to 3= 2*3^5
or 2J= 486
so that J = 243
kindly approve :))
Vikas TU
14149 Points
2 years ago
Dear student 
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Good Luck 

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