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forsale [732]
3 years ago
11

WILL GIVE BRAINLIEST

Mathematics
1 answer:
Paul [167]3 years ago
7 0
256.
EXPLANATION:

When you are using exponents, you are basically just doing repeated multiplication.

Whatever the exponent (smaller number is) is how many times you multiply the base number by itself.

So 4 ^4 is 4 x 4 x 4 x 4. (4 fours.)

So 4 x 4 x 4 x 4 is 256.
HAVE A GUD DAY
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A farmer sold 1/4 of his 1500 flock of sheep. how many sheep dd he sell?<br>​
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Calculus 3 help please.​
Reptile [31]

I assume each path C is oriented positively/counterclockwise.

(a) Parameterize C by

\begin{cases} x(t) = 4\cos(t) \\ y(t) = 4\sin(t)\end{cases} \implies \begin{cases} x'(t) = -4\sin(t) \\ y'(t) = 4\cos(t) \end{cases}

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ds = \sqrt{x'(t)^2 + y'(t)^2} \, dt = \sqrt{16(\sin^2(t)+\cos^2(t))} \, dt = 4\,dt

and the integral reduces to

\displaystyle \int_C xy^4 \, ds = \int_{-\pi/2}^{\pi/2} (4\cos(t)) (4\sin(t))^4 (4\,dt) = 4^6 \int_{-\pi/2}^{\pi/2} \cos(t) \sin^4(t) \, dt

The integrand is symmetric about t=0, so

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Substitute u=\sin(t) and du=\cos(t)\,dt. Then we get

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with 0\le t\le1. Then

ds = \sqrt{3^2+4^2} \, dt = 5\,dt

and

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u = 3t-2 \implies du = 3\,dt \\\\ dv = e^{4t} \, dt \implies v = \frac14 e^{4t}

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