₀¹ [f (x) g " (x) - f " (x) g (x)] dx is equal to : [Given f(0) = g(0) = 0]

Correct Answer is : f (1) g ' (1) - f ' (1) g (1)

Correct Answer is : f (1) g ' (1) - f ' (1) g (1)

Test Index

VITEEE 2017 Paper

Section: Mathematics

Question : 97 of 125

Marks: +1, -0

\int\limits_{0}^{1}

[Given f(0) = g(0) = 0]

Solution:

Integrating by parts.

∫ f (x) g " (x) dx - ∫ f " (x) g (x) dx

= f (x) g ' (x) - ∫ f ' (x) g ' (x) dx - f ' (x) g (x) + ∫ f ' (x) g ' (x) dx

= f (x) g ' (x) - f ' (x) g (x)

Hence ,

\int\limits_{0}^{1}

f (x) g " (x) dx -

\int\limits_{0}^{1}

f " (x) g (x) dx

= f (1) g ' (1) - f ' (1) g (1) - f (0) g ' (0) + f ' (0) g (0)

= f (1) g ' (1) - f ' (1) g (1)

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