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Integration by Parts

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Question

If in the product of two functions, one of the function is not directly integrable $(e . g . log (x |, {sin}^{- 1} x, etc .)$ , then we take it as a first function under ILATE.

A

False

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B

True

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Solution

The correct option is B True

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Similar questions

f : A \to B

be a function defined by

y = f (x)

where f is a bijective function, means f is injective (one-one) as well as surjective (onto), then there exist a unique mapping

g : B \to A

f (x) = y

g (y) = x \forall x ϵ A, y ϵ B

Then function g is said to be inverse of f and vice versa so we write

g = f^{- 1} : B \to A [{f (x), x} : {x, f (x)} ϵ f^{- 1}]

when branch of an inverse function is not given (define) then we consider its principal value branch.

Which of the following is not correct?

Q. Considering land as a factor of production give two of its functions.

Q. The function

2 x^{2} - log x

is a decreasing function if

x

belongs to the interval

Q. Assertion(A):

f (x) = log (x - 2) + log (x - 3)

g (x) = log (x - 2) (x - 3)

f (x) = g (x)

Reason (R): Two functions

f (x)

g (x)

are said to be equal if they are defined on the same domain

A

and the co-domain

B

f (x) = g (x) \forall x \in A

Q. Assertion :The IUPAC name of citric acid is

2 - h y d r o x y - p r o p a n e - 1, 2, 3 - t r i c a r b o x y l i c

acid. Reason: When an unbranched C atom is directly linked to more than two like-functional groups, then it is named as a derivative of the parent alkane which does not include the C atoms of the functional groups.

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