a function whose derivative is sine x and whose graph passes through the point 0 2
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Answer
Correct option is
C
f(x)=−(1/3)[(1−x
2
)
3/2
+
3
8
]
f(x)=∫x
1−x
2
dx
Let (1−x
2
)=z⟹−2xdx=dz⟹dx=
2
1
dz
f(x)=∫
2
−1
z
dz=−
3
1
(1−x
2
)
3/2
+c
On satisfying with (0,7/3) we get c=8/3
=−
3
1
(1−x
2
)
3/2
+8/3
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