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Question

The equation of a curve passing through origin is given by y=x3 cos x4 dx. If the equation of the curve is written in the form x = g(y), then

A
g(y)=3sin1(4y)
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B
g(y)=sin1(4y)
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C
g(y)=4sin1(4y)
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D
None of these
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Solution

The correct option is C g(y)=4sin1(4y)
We have, y=x3 cos x4 dx=14cos t dt[Put x4=tx3 dx=14dt]=14sin t+C=14sin x4+C
Since the curve passes through (0, 0) ,therefore C=0
y=14sin x4x4=sin1(4y)x=4sin1(4y)

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