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user100 [1]
3 years ago
11

Evaluate ModifyingBelow Integral from nothing to nothing With Upper C xy dx plus left parenthesis x plus y right parenthesis dy

∫ C xy dx+(x+y)dy along the curve y equals 4 x squared y=4x2 from left parenthesis negative 3 comma 36 right parenthesis (−3,36) to left parenthesis 1 comma 4 right parenthesis (1,4). ModifyingBelow Integral from nothing to nothing With Upper C xy dx plus left parenthesis x plus y right parenthesis dy ∫ C xy dx+(x+y)dy equals = nothing ​(Type an integer or a simplified​ fraction.)
Mathematics
1 answer:
Zepler [3.9K]3 years ago
7 0

Parameterize the curve by

\begin{cases}x(t)=t\\y(t)=4t^2\end{cases}

with -3\le t\le1. Then

\displaystyle\int_Cxy\,\mathrm dx+(x+y)\,\mathrm dy

=\displaystyle\int_{-3}^14t^3\,\mathrm dt+(t+4t^2)(8t\,\mathrm dt)

=\displaystyle\int_{-3}^1(8t^2+36t^3)\,\mathrm dt=\boxed{-\frac{1936}3}

You might be interested in
Please help find them <br>1 AB<br><br>2 BC​
spin [16.1K]

Answer:

AB ≈ 15.7 cm, BC ≈ 18.7 cm

Step-by-step explanation:

(1)

Using the Cosine rule in Δ ABD

AB² = 12.4² + 16.5² - (2 × 12.4 × 16.5 × cos64° )

       = 153.76 + 272.25 - (409.2 cos64° )

       = 426.01 - 179.38

       = 246.63 ( take the square root of both sides )

AB = \sqrt{246.63} ≈ 15.7 cm ( to 1 dec. place )

(2)

Calculate ∠ BCD in Δ BCD

∠ BCD = 180° - (53 +  95)° ← angle sum in triangle

∠ BCD = 180° - 148° = 32°

Using the Sine rule in Δ BCD

\frac{BC}{sin53} = \frac{BD}{sin32} = \frac{12.4}{sin32} ( cross- multiply )

BC × sin32° = 12.4 × sin53° ( divide both sides by sin32° )

BC = \frac{12.4sin53}{sin32} ≈ 18.7 cm ( to 1 dec. place )

         

6 0
2 years ago
Observa las ilustraciones y escribe la fracción que corresponde a cada giro
frosja888 [35]

Answer:

1: 7/12 2:1/3 3:1/2 4:1/3 5:5/8 6:1/2 7:6/10 8:1/1 9:1/4

Step-by-step explanation:

lo saque de otro trabajo igual.

6 0
2 years ago
How to find volume of a rectangular prism ith surface area, width and length but no height
Tpy6a [65]
Volume equals width times height times length
8 0
3 years ago
Which expression is equivalent to 2(x+7)-18+4/5 ?
Vadim26 [7]

Answer:

4.7/5

Step-by-step explanation:

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2 years ago
What is 12 ten thousand 8 thousands 14 hundreds 7 ones
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Answer:

Eight thousand fourteen hundred twelve and seven

5 0
3 years ago
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