Question

f(n) = 3 cosec^2x + 2 sinx integrate ​the function

Answer 1

Explanation:

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Asked on December 30, 2019 by Akhil Deb

If

∫cosec 2xdx=

f(g(x))+

C,

then

THIS QUESTION HAS MULTIPLE CORRECT OPTIONS

A range

g(x)=

(−∞,∞)

B dom

g(x)=

(−∞,∞)∼

{0}

C

g ′

sec 2

D

x∈

(0,∞)

f ′

x

1

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ANSWER

cosec(2x)=

sin(2x)

1

=

2sin(x)cos(x)

1

=

2sin(x)cos

2

(x)

cosx

=

2tanx

1+tan

2

x

∫cosec(2x)dx==

∫

2tanx

1+tan

2

x

dx

Now put

tan(x)=

t⇒

dt=

sec 2

(1+

t 2

(1+

tan 2

∫

2t

1+t

2

×

1+t

2

dt

=

2

1

∫

t

dt

=

2

1

lnt+ C

=

2

1

ln(tanx)+

C

=

ln

tanx

+

C

2

1

lntan(x)

g(x)= tanx

Since, tanx is not defined at 0

So, domain of

g(x)=

(−∞,∞)−

{0}

Range of g(x) is (−∞,∞)

g ′