Math, asked by poonamrathod24, 6 months ago

① Integration of 2y
dy?​

Answers

Answered by debdattagupta177
1

Answer:

Let I=∫

1+y

2

⋅2ydy

Let u=1+y

2

, then du=2y dy.

I=∫u

1/2

du

=

(1/2)+1

u

1/2

+1

[Integrate, using rule no. 3 with n=1/2]

=

3

2

u

3/2

+C [Simpler form]

=

3

2

(1+y

2

)

3/2

+C [Replace u by 1+y

2

].

Answered by AneesKakar
1

The integration of 2ydy is y² + c.

Procedure:

To solve the given integral we can use the integration rule for polynomials:

                                      \int\limits{x^{n} } \, dx =\frac{x^{n+1} }{n+1} +c

We can now use the above formula to solve the integral:

                                          I=\int\limits {2y} \, dy\\\\=2\int\limits {y} \, dy \\\\=2(\frac{y^{2} }{2} )+c\\\\=y^{2} +c

Hence, the integration of 2ydy is y² + c.

#SPJ2

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