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kkurt [141]
3 years ago
15

Given: x is an integer. Conjecture: -x is negative. Counterexample:

Mathematics
1 answer:
Setler [38]3 years ago
8 0

Answer:

-1,-2,-3,-4,-5,-6,-7,-8,-9

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Let

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with

u = e^{-2x} \implies du = -2 e^{-2x} \, dx \\\\ dv = \cos(2x) \, dx \implies v = \dfrac12 \sin(2x)

Then

\displaystyle I = \frac12 e^{-2x} \sin(2x) + \int e^{-2x} \sin(2x) \, dx + C

Integrate by parts again, this time with

u = e^{-2x} \implies du = -2 e^{-2x} \, dx \\\\ dv = \sin(2x) \, dx \implies v = -\dfrac12 \cos(2x)

so that

\displaystyle I = \frac12 e^{-2x} \sin(2x) - \frac12 e^{-2x} \cos(2x) - \int e^{-2x} \cos(2x) \, dx + C\\\\ \implies I = \frac{\sin(2x)-\cos(2x)}{2e^{2x}} - I + C \\\\ \implies 2I = \frac{\sin(2x) - \cos(2x)}{2e^{2x}} + C \\\\ \implies I = \boxed{\frac{\sin(2x) - \cos(2x)}{4e^{2x}} + C}

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1 year ago
A rainwater collection tank is shaped like a cylinder with a diameter of 4 ft and height of 6 ft what is its volue
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3 years ago
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Mode = 11

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I need help due in 20 min thank I will help u to
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5*7*3
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