Beta Question Bank for Engineering: Mathematics>Chapter 31 - Definite Integration>EXERCISE-1>Q 18

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The value of the definite integral $\int_{0}^{1} (1 + e^{- x^{2}}) d x$ is

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Important Questions on Definite Integration

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Beta Question Bank for Engineering: Mathematics>Chapter 31 - Definite Integration>EXERCISE-1>Q 19

\int_{- π}^{π} {(\cos a x - \sin b x)}^{2} d x

where

a

and

b

are integer is equal to-

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Beta Question Bank for Engineering: Mathematics>Chapter 31 - Definite Integration>EXERCISE-1>Q 20

The value of

\int_{- π}^{π} (1 - x^{2}) \sin x \cos^{2} x d x

is-

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Beta Question Bank for Engineering: Mathematics>Chapter 31 - Definite Integration>EXERCISE-1>Q 21

The value of

\int_{π}^{2 π} [2 \sin x] d x

is equal to (where [.] represents the greatest integer function)

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Beta Question Bank for Engineering: Mathematics>Chapter 31 - Definite Integration>EXERCISE-1>Q 22

If

\int_{0}^{f (x)} t^{2} dt = x \cos π x

then

f^{'} (9)

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Beta Question Bank for Engineering: Mathematics>Chapter 31 - Definite Integration>EXERCISE-1>Q 23

Let $f : R \to R$ be a differentiable function and $f (1) = 4$ .

Then, the value of $\lim_{x \to 1} \int_{4}^{f (x)} \frac{2 t}{x - 1} d t$ is

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Beta Question Bank for Engineering: Mathematics>Chapter 31 - Definite Integration>EXERCISE-1>Q 24

If

g (x) = \int_{0}^{x} \cos^{4} t d t

, then

g (x + π)

equals

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Beta Question Bank for Engineering: Mathematics>Chapter 31 - Definite Integration>EXERCISE-1>Q 25

For

n \in N

, the value of the definite integral

\int_{0}^{n π + V} (\sqrt{\frac{1 + \cos 2 x}{2}}) d x

where

\frac{π}{2} < V < π

is-

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Beta Question Bank for Engineering: Mathematics>Chapter 31 - Definite Integration>EXERCISE-2>Q 1

Area enclosed by the curve

y = \sin x

between

x = 2 n π

to

x = 2 (n + 1) π

is-