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

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IMPORTANT

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$\int \frac{d x}{\sqrt{x - x^{2}}}$ equals, where $x \in (\frac{1}{2}, 1)$ -

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Important Questions on Indefinite Integration

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IMPORTANT

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

EASY

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IMPORTANT

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

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IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 30 - Indefinite Integration>EXERCISE-3>Q 12

If

f (x) = \tan^{- 1} x + \ln \sqrt{1 + x} - \ln \sqrt{1 - x}

and

\frac{1}{2} \int f^{'} (x) d (x^{4}) = - \ln (1 - x^{n}) + C

, then the value of

n

is

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IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 30 - Indefinite Integration>EXERCISE-3>Q 13

If

\int \sqrt{\frac{cosec x - \cot x}{cosec x + \cot x}} \cdot \frac{\sec x}{\sqrt{1 + 2 \sec x}} d x = \sin^{- 1} (\frac{1}{k} \sec^{2} \frac{x}{2}) + C

then the value of

k

is