3 years ago

Determine whether the function are inverse. F(x)=6x+l;g(x)=6x-1

Mathematics

1 answer:

sesenic [268]3 years ago

7 0

Nope, inverse of first function is
f^-1(x)= (x-1)/6

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We have

$\displaystyle \int_C \vec f \cdot d\vec r = \int_0^{\frac{3\pi}2} \vec f(\vec r(t)) \cdot \dfrac{d\vec r}{dt} \, dt$

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so the line integral is equilvalent to

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$\displaystyle \int_C \vec f \cdot d\vec r = \int_0^{\frac{3\pi}2} (3\sin(2t) + t) \, dt$

$\displaystyle \int_C \vec f \cdot d\vec r = \left(-\frac32 \cos(2t) + \frac12 t^2\right) \bigg_0^{\frac{3\pi}2}$

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