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Integral Calculus> Integrate the following with respect to x...

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

meenu s nair , 5 Years ago

Grade 10

2 Answers

Aditya Gupta

Last Activity: 5 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+e^x)dx

or J= _-3∫³(5x⁴/1+e^x)dx ….....(2)

now, write (1) as J= _-3∫³(5e^x.x⁴/1+e^x)dx …......(3)

add (2) and (3)

2J= _-3∫³(5x⁴/1+e^x)*(1+e^x)dx = _-3∫³5x⁴dx = x^5| – 3 to 3= 2*3^5

or 2J= 486

so that J = 243

kindly approve :))

Vikas TU

Last Activity: 5 Years ago

Dear student

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https://www.askiitians.com/iit-jee-indefinite-integral/solved-examples-of-indefinite-integral.html

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