Beta Question Bank for Engineering: Mathematics>Chapter 30 - Indefinite Integration>EXERCISE-2>Q 18

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Let $f^{'} (x) = 3 x^{2} \cdot \sin \frac{1}{x} - x \cos \frac{1}{x}, x \neq 0, f (0) = 0, f (\frac{1}{π}) = 0$ , then which of the following is/are not correct.

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Important Questions on Indefinite Integration

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Beta Question Bank for Engineering: Mathematics>Chapter 30 - Indefinite Integration>EXERCISE-2>Q 19

\int \frac{1}{x^{2} - 1} \ln \frac{x - 1}{x + 1} d x

equals -

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Beta Question Bank for Engineering: Mathematics>Chapter 30 - Indefinite Integration>EXERCISE-2>Q 20

\int \frac{d x}{\sqrt{x - x^{2}}}

equals, where

x \in (\frac{1}{2}, 1)

-

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Beta Question Bank for Engineering: Mathematics>Chapter 30 - Indefinite Integration>EXERCISE-2>Q 21

\int \frac{\sin 2 x}{\sin^{4} x + \cos^{4} x} d x

is equal to

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Beta Question Bank for Engineering: Mathematics>Chapter 30 - Indefinite Integration>EXERCISE-2>Q 22

Primitive of

\sqrt{1 + 2 \tan x (\sec x + \tan x)}

w.r.t.

x

is

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Beta Question Bank for Engineering: Mathematics>Chapter 30 - Indefinite Integration>EXERCISE-2>Q 23

\int \sin 2 x d x

equals -

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Beta Question Bank for Engineering: Mathematics>Chapter 30 - Indefinite Integration>EXERCISE-2>Q 24

\int \frac{d x}{x^{3} (1 - \frac{1}{2 x^{2}})}

equals -

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Beta Question Bank for Engineering: Mathematics>Chapter 30 - Indefinite Integration>EXERCISE-2>Q 25

If

\int e^{3 x} \cos 4 x d x = e^{3 x} (A \sin 4 x + B \cos 4 x) + C

, then

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Beta Question Bank for Engineering: Mathematics>Chapter 30 - Indefinite Integration>EXERCISE-3>Q 11

If

\int [\frac{\sqrt{x^{2} + 1} [\ln (x^{2} + 1) - 2 \ln (x)]}{x^{4}}] d x = \frac{(x^{2} + 1) \sqrt{x^{2} + 1}}{a^{2} x^{3}} (2 - a \ln (1 + \frac{1}{x^{2}})) + c

then the value of

a

is