Question

find the double integral
the integral from 5 to 4 the integral from 5 to 4 (4x+y)^-1

Answer 1

- integrating \(\frac1{4x+y}\) with respect to \(y\) gives \(\ln(4x+y)\).
- a primitive of \(\ln(x)\) is \(x\ln(x)- x \). This might help, I didn't do it but im confident it's what you need.

Answer 2

im not really sure what you did im just had my first lecture on double integrals today so im not sure how to solve it

Answer 3

Marry me, I'm an Asian.

Answer 4

you can choose the order of integration. I'll fix it to this: \(\int_4^5(\int_4^5 \dots\,dy)dx\)

You will first evaluate what's inside the parenthesis.

Answer 5

since it's an integration of the variable \(y\) you consider \(x\) as constant. A primitive of the function is ln(4x+y).
-> the parenthesis is equal to \(\ln(4x+5) - \ln(4x+4)\).
Then you can split the integrals and use "normal" integration.

Answer 6

so the equation you typed is my function and i first have to find the integral with respect to y and whatever i get from there i take the integral with respect to x

Answer 7

yes. in general, the parenthesis , after integrating once, still contains one variable.
Here \(dy\) is in the parenthesis. After comupting this, all \(y\)'s have disappeared. only \(x\)'s remain.

Answer 8

ok so the integral for the above functions is 1/4x+5 - 1/4x+4 right

Answer 9

which integral? I don't think this function appears in the answer.


One part of the answer is
\[\int_4^5 \ln(4x+5) \,dx = \int_{21}^{25} \ln(u) \frac14\,du\\
= \left[ u\ln u - u \right]_{21}^{25}
\]i think.

Answer 10

hi im here!!

Answer 11

i forgot \(\frac14\)

Answer 12

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