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CaHeK987 [17]
4 years ago
10

Evaluate the line integral c f · dr, where c is given by the vector function r(t). f(x, y, z) = (x + y2) i + xz j + (y + z) k, r

(t) = t2 i + t3 j − 2t k, 0 ≤ t ≤ 2 $$ correct: your answer is correct.
Mathematics
1 answer:
Mademuasel [1]4 years ago
6 0

\vec r(t)=t^2\,\vec\imath+t^3\,\vec\jmath-2t\,\vec k

\mathrm d\vec r=(2t\,\vec\imath+3t^2\,\vec\jmath-2\,\vec k)\,\mathrm dt

\vec f(x,y,z)=(x+y^2)\,\vec\imath+xz\,\vec\jmath+(y+z)\,\vec k

\vec f(x(t),y(t),z(t))=(t^2+t^6)\,\vec\imath-2t^3\,\vec\jmath+(t^3-2t)\,\vec k

The line integral is

\displaystyle\int_C\vec f\cdot\mathrm d\vec r=\int_0^2\bigg((t^2+t^6)\,\vec\imath-2t^3\,\vec\jmath+(t^3-2t)\,\vec k\bigg)\cdot(2t\,\vec\imath+3t^2\,\vec\jmath-2\,\vec k)\,\mathrm dt

=\displaystyle\int_0^2(2t^7-6t^5+4t)\,\mathrm dt=\boxed{8}

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Step-by-step explanation:

(-2a² + s)(5a² - 6s)

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3 years ago
Write and solve the equation that represents in the sentence below the product of 18 and a number is 109point statements are cor
katen-ka-za [31]

Answer:

6 1/18

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Step-by-step explanation:

18x = 109

Divide both sides by 18

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3 years ago
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Mandarinka [93]
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7 0
4 years ago
Read 2 more answers
What are the x-intercepts of the graph of the function f(x) = x2 + 4x – 12? (–6, 0), (2,0) (–2, –16), (0, –12) (–6, 0), (–2, –16
Margaret [11]

Answer:

(-6, 0) and (2, 0)

Step-by-step explanation:

To find the x-intercepts, we can factor the expression:

f(x) = x² + 4x - 12

2 factors of -12 that add up to 4 are 6 and -2

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Set each factor equal to 0 and solve for x:

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x = -6

x - 2 = 0

x = 2

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4 0
3 years ago
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