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Integrate the following with respect to x: -3 ∫ 3 (5x 4 /1+e -x )dx =
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)dxor 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*3^5or 2J= 486so that J = 243kindly approve :))
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