I=π2−π/4∫π/4(1+esinx)(2−cos2x)dx then find 27I2

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$I = \frac{2}{π} - π / 4 \int π / 4 \frac{d x}{( 1 + e ^{s i n x} ) ( 2 - cos 2 x )}$ then find $27 I^{2}$

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I = \frac{2}{π} - π / 4 \int π / 4 \frac{d x}{( 1 + e ^{s i n x} ) ( 2 - cos 2 x )}

then find

27 I^{2}

6 mins ago

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Practice questions from similar books

Question 1

Let

f_{1} : R \to R, f_{2} : (- \frac{π}{2}, \frac{π}{2}) \to R f_{3} : (- 1, e^{\frac{π}{2}} - 2) \to R

and

f_{4} : R \to R

be functions defined by\displaystyle{{f}_{{1}}{\left({x}\right)}}={\sin{{\left(\sqrt{{{1}-{e}^{{-{{x}}}}^{2}}}\right)}}},(ii)

f_{2} (x) = {\frac{∣ sin x ∣}{tan ^{- 1} x} if x \neq = 01 if x = 0,

where the inverse trigonometric function

tan^{- 1} x

assumes values in

(\frac{π}{2}, \frac{π}{2})

,(iii)

f_{3} (x) = [sin ((lo g)_{e} (x + 2))]

, where, for

t \in R

[t]

denotes the greatest integer less than or equal to

t

,(iv)

f_{4} (x) = {x^{2} sin (\frac{1}{x}) if x \neq = 00 if x = 0

.LIST-I LIST-IIP. The function

f_{1}

is 1. NOT continuous at

x = 0

Q. The function

f_{2}

is 2. continuous at

x = 0

and NOTR. The function

f_{2}

is differentiable at

x = 0

S. The function

f_{2}

is 3. differentiable at

x = 0

and itsis NOT continuous at

x = 0

4. differentiable at

x = 0

and itsderivative is continuous at

x = 0

The correct option is

P \to 2; Q \to 3; R \to 1; S \to 4

(b)

P \to 4; Q \to 1; R \to 2; S \to 3

(c)

P \to 4; Q \to 2; R \to 1; S \to 3

(d)

P \to 2; Q \to 1; R \to 4; S \to 3

View solution

Question 2

Let

f : (0, \infty) R

be given by

f (x) = \int_{\frac{1}{x}}^{x} \frac{e ^{- (t + \frac{1}{t})} d t}{t},

then (a)

f (x)

is monotonically increasing on

[1, \infty)

(b)

f (x)

is monotonically decreasing on

(0, 1)

(c)

f (2^{x})

is an odd function of

x

R

View solution

Question 3

PARAGRAPH AThere are five students

S_{1}, S_{2}, S_{3}, S_{4}

and

S_{5}

in a music class and for them there are five seats

R_{1}, R_{2}, R_{3}, R_{4}

and

R_{5}

arranged in a row, where initially the seat

R_{i}

is allotted to the student

S_{i}, i = 1, 2, 3, 4, 5

. But, on the examination day, the five students are randomly allotted five seats. For

i = 1, 2, 3, 4,

let

T_{i}

denote the event that the students

S_{i}

and

S_{i + 1}

do NOT sit adjacent to each other on the day of the examination. Then, the probability of the event

T_{1} \cap T_{2} \cap T_{3} \cap T_{4}

\frac{1}{15}

(b)

\frac{1}{10}

(c)

\frac{7}{60}

(d)

\frac{1}{5}

View solution

Question 4

In R', consider the planes

P_{1}, y = 0

and

P_{2} : x + z = 1

. Let

P_{3}

, be a plane, different from

P_{1}

, and

P_{2}

, which passes through the intersection of

P_{1}

, and

P_{2}

. If the distance of the point

(0, 1, 0)

from

P_{3}

, is

1

and the distance of a point

(α, β, γ)

from

P_{3}

2

, then which of the following relation is (are) true ?

View solution

Question Text

I = \frac{2}{π} - π / 4 \int π / 4 \frac{d x}{( 1 + e ^{s i n x} ) ( 2 - cos 2 x )}

then find

27 I^{2}

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I=π2​−π/4∫π/4​​(1+esinx)(2−cos2x)dx​ then find 27I2

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Practice questions from similar books

$I = \frac{2}{π} - π / 4 \int π / 4 \frac{d x}{( 1 + e ^{s i n x} ) ( 2 - cos 2 x )}$ then find $27 I^{2}$