GATE Mechanical Engineering (ME) 2019 Shift 1 Solved Paper

Question : 46 of 65

Marks: +1, -0

The value of the following definite integral is __________ (round off to three decimal places)

∫↙{1}↖{e}(x \ln x) d x

Solution:

we have to use integration by parts in this

∫ u v d x=u ∫ v d x-∫[\;{d u}/{d x} ∫ v d x] d x

Using the ILATE formula,
We have

u=\ln x

and

v=x

∫ x \ln x d x=\ln x ∫ x d x-∫ \;{1}/{x} ∫ x d x d x

(\;{x^{2}}/{2} \ln x-\;{x^{2}}/{4})_{1}^{e}=\;{e^{2}+1}/{4}=2.097

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