NDA Maths Mock Test – 01 – Q93 - https://blog.perfectrank.in

Question:

int e^x (f(x) + f'(x)) is equal to

Options:

e^x + f(x) + C
e^x f(x) + C
e^f(x) + f(e^x) + C
e^x (f(x) – f'(x)) + C

e^x + f(x) + C
e^x f(x) + C
e^f(x) + f(e^x) + C
e^x (f(x) – f'(x)) + C

Correct Answer: b)

Explanation:

‘
! Jet (f(z) + f'(z))dz = e® f(z)dz + e® f'(x)dz ‘
1 = f(z)e* — f'(z)e*dz + f'(z)e”dz + C
‘ (Using By Part, taking f(x) as I function)
= f(z)e® + C
‘ It is a standard formula.
) 94. H
(d) log sinz + cosz + C
‘

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