Question

The function f(x) whose derivative is sin x and whose graph passes through the point(0, 2)​

Answer 1

Answer:

=x

1−x

2

⇒dy=x

1−x

2

dx

∫dy=∫x

1−x

2

dx

Let u=1−x

2

⇒du=−2xdx⇒ dx=−

2x

1

du

∴∫x

1−x

2

dx=∫x(−

2x

1

)du

u

=−

2

1

∫

u

du

Now, ∫

u

du=

3

2

u

3/2

∴−

2

1

∫

u

du=−

3

1

u

3/2

=

3

1

(1−x

2

)

3/2

∴y=−

3

1

(1−x

2

)

3/2

+c

Now, this curve passes through (0,

3

7

)

∴

3

7

=−

3

1

(1−0)

3/2

+c ⇒

3

7

=−

3

1

+c ⇒c=

3

8

∴

y=−

3

1

(1−x

2

)

3/2

+

3

8