Math, asked by lnt7519, 1 year ago

please solve this question and explain it​

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Answers

Answered by kingaj001744
0

answer

x

4

x

2

1

d

x

=

1

3

x

3

+

x

+

1

2

ln

x

1

x

+

1

+

c

Explanation:

For the integrand  

x

4

x

2

1

, we perform a long division to get it into an integrable form.

x

4

x

2

1

=

x

4

1

+

1

x

2

1

=

(

x

2

1

)

(

x

2

+

1

)

x

2

1

+

1

x

2

1

=

=

x

2

+

1

+

1

(

x

+

1

)

(

x

1

)

We now perform a partial fraction decomposition on the 2nd term

1

(

x

+

1

)

(

x

1

)

=

(

x

+

1

)

(

x

1

)

2

(

x

+

1

)

(

x

1

)

=

x

+

1

2

(

x

+

1

)

(

x

1

)

x

1

2

(

x

+

1

)

(

x

1

)

=

1

2

(

x

1

)

1

2

(

x

+

1

)

So

x

4

x

2

1

=

x

2

+

1

+

1

2

(

x

1

)

1

2

(

x

+

1

)

and we can now integrate:

x

4

x

2

1

d

x

=

x

2

+

1

+

1

2

(

x

1

)

1

2

(

x

+

1

)

d

x

=

1

3

x

3

+

x

+

1

2

ln

|

x

1

|

1

2

ln

|

x

+

1

|

+

c

=

1

3

x

3

+

x

+

1

2

ln

x

1

x +1

∣ +c

Answered by itzXtylishAbhi
1

Step-by-step explanation:

The spectrum of light emitted by a glowing solid is

A) Continuous spectrum B) Line spectrum C) Band spectrum D) Absorption spectrum

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