The function f(x) whose derivative is sin x and whose graph passes through the point(0, 2)
Answers
Answered by
9
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
Similar questions