Please help me fast and show all your work please thx

Mathematics

2 answers:

Dafna11 [192]3 years ago

8 0

Answer:

Step-by-step explanation:

$Area=\frac{1}{2}*(8+5)*2\\\\=\frac{1}{2}*13*2\\\\=13mm^{2}$

olga_2 [115]3 years ago

4 0

Answer:

Step-by-step explanation:

1/2x(8+5)x2

1/2×13×2

=13

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∫c<br> x sin y ds, C is the line segment from (0, 1) to (3, 5)

Mnenie [13.5K]

Parameterize the line segment $C$ by

$\mathbf r(t)=\langle x(t),y(t)\rangle=(1-t)\langle0,1\rangle+t\langle3,5\rangle=\langle3t,1+4t\rangle$

where $t\in[0,1]$ . Then

$\mathrm ds=\|\mathbf r'(t)\|\,\mathrm dt$
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$\mathrm ds=5\,\mathrm dt$

So the integral is

$\displaystyle\int_Cx\sin y\,\mathrm ds=5\int_0^1x(t)\sin y(t)\,\mathrm dt$
$=\displaystyle5\int_0^13t\sin(1+4t)\,\mathrm dt$
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