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3 years ago

Find he measure of xi 5x-2 H

Mathematics

1 answer:

Aleks [24]3 years ago

5 0

I think it’s-10. Hope it’s right.

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Evaluate the integral by making an appropriate change of variables.

VARVARA [1.3K]

By inspecting the integrand, the "obvious" choice for substitution would be

u = y + x

v = y - x

Solving for x and y, we would have

x = (u - v)/2

y = (u + v)/2

in which case the Jacobian and its determinant are

$J=\begin{bmatrix}x_u&x_v\\y_u&y_v\end{bmatrix}=\dfrac12\begin{bmatrix}1&-1\\1&1\end{bmatrix}\implies|\det J|=\left|\dfrac12\right|=\dfrac12$

The trapezoid R has two of its edges on the lines x + y = 8 and x + y = 9, so right away, we have 8 ≤ u ≤ 9.

Then for v, we observe that when x = 0 (the lowest edge of R), v = y ; similarly, when y = 0 (the leftmost edge of R), v = -x. So

-x ≤ v ≤ y

-(u - v)/2 ≤ v ≤ (u + v)/2

-u + v ≤ 2v ≤ u + v

-u ≤ v ≤ u

So, the integral becomes

$\displaystyle\iint_R5\cos\left(7\frac{y-x}{y+x}\right)\,\mathrm dA=\int_8^9\int_{-u}^u\frac52\cos\left(\frac{7v}u\right)\,\mathrm dv\,\mathrm du$

$=\displaystyle\frac52\int_8^9\frac u7(\sin7-\sin(-7))\,\mathrm du$

$=\displaystyle\frac57\sin7\int_8^9u\,\mathrm du$

$=\displaystyle\frac5{14}\sin7(9^2-8^2)=\boxed{\frac{85}{14}\sin7}$

4 0

2 years ago

In 4.59 what does the nine stand for?

Kisachek [45]

The 9 stands for hundredths

4 0

3 years ago

Read 2 more answers

Somebody please help me answer this

Inga [223]

-2x+4 I am pretty sure

8 0

3 years ago

Please help:((

kolezko [41]

Answer:

1/8 = 0.125

3/5= 0.60

30%=0.3

0.45=9/20

1.5=150%

Hey try to do these question by your self next time OwO

4 0

3 years ago

A jacket is reduced by 40% in a sale to £36 what wad its original price

VladimirAG [237]

$36x 40% =$14.40 was taken off
$36+$14.40=$50.40 was original price
Hope this helps

7 0

3 years ago