from Want to five. So there's a support. The dog with the ground getting groceries from 0 to 3 off as choir. Oh, I plus flies. Why, it's to parent there. So we have tea X do you want? So do these. You know, this is so simple because Siri however, why here and why here and that kind of redundant the candle factory stays. I'm gonna leave the I won't leave the integration process and what they say until the far off. Uh, it's crap plus five. That's why it just felt right there, white out. So ah, sedition digression can become like, you know, taking the the integral off this so we can have two functions. Every we have to, uh, supports here. So we now have toe do the infest integration with restaurants or the X. So it means we I assume that why is in constant, you know, and then we does integrate what is yet. So if we integrate this, we are gonna have on the girl from one to fine. I just Oh, far X to the power trees. About three plus five x. That's five X. Here we have the wine. Wait. Put this support from 0 to 3? No. Do you? Why? Because so we have finished still there with the ex. So it is not a matter to prepare the X bye three, You know, we apply the integration. So taking this out, I think I should be able to have being God like you, Raisa. Really want to race too tense. That's just a theory. Is this okay? So now we have I think, in this you have This is not the quote toe the integral from 1 to 5. Oh. Oh, So you're gonna have a trance itself here. About three Ridge is my just my last 15 and, uh, man plus 15 24 story of truancy for Why do you want So this is my sample integral to Justin. Martyr off. You think? Written 20 for while you two respectable t y. And you're gonna have to answer for why square you got it. Bye. So from Wirz of honey does our support, and, uh, this is equal toe. So into parent is US 25. Plus what? I was ordered money's worth. And, uh, I'm going to the second pitch. There's gonna be you quote toe four times turns you fool. Uh, 12 times 24 is, uh do him 200 eh? It's It's just so so it it's sorry about this Supposed to be, so it's picked. Okay, So I will come to Dio Clara p do about this because currently, just using my iPod be by my kabira and into every place where I could get Oh, that. That's you, Ted. Uh, you know, uh, device to do that?

## Discussion

## Video Transcript

from Want to five. So there's a support. The dog with the ground getting groceries from 0 to 3 off as choir. Oh, I plus flies. Why, it's to parent there. So we have tea X do you want? So do these. You know, this is so simple because Siri however, why here and why here and that kind of redundant the candle factory stays. I'm gonna leave the I won't leave the integration process and what they say until the far off. Uh, it's crap plus five. That's why it just felt right there, white out. So ah, sedition digression can become like, you know, taking the the integral off this so we can have two functions. Every we have to, uh, supports here. So we now have toe do the infest integration with restaurants or the X. So it means we I assume that why is in constant, you know, and then we does integrate what is yet. So if we integrate this, we are gonna have on the girl from one to fine. I just Oh, far X to the power trees. About three plus five x. That's five X. Here we have the wine. Wait. Put this support from 0 to 3? No. Do you? Why? Because so we have finished still there with the ex. So it is not a matter to prepare the X bye three, You know, we apply the integration. So taking this out, I think I should be able to have being God like you, Raisa. Really want to race too tense. That's just a theory. Is this okay? So now we have I think, in this you have This is not the quote toe the integral from 1 to 5. Oh. Oh, So you're gonna have a trance itself here. About three Ridge is my just my last 15 and, uh, man plus 15 24 story of truancy for Why do you want So this is my sample integral to Justin. Martyr off. You think? Written 20 for while you two respectable t y. And you're gonna have to answer for why square you got it. Bye. So from Wirz of honey does our support, and, uh, this is equal toe. So into parent is US 25. Plus what? I was ordered money's worth. And, uh, I'm going to the second pitch. There's gonna be you quote toe four times turns you fool. Uh, 12 times 24 is, uh do him 200 eh? It's It's just so so it it's sorry about this Supposed to be, so it's picked. Okay, So I will come to Dio Clara p do about this because currently, just using my iPod be by my kabira and into every place where I could get Oh, that. That's you, Ted. Uh, you know, uh, device to do that?

## Recommended Questions

Evaluate each iterated integral. (Many of these use results from Exercises 1-10 ).

$$\int_{1}^{5} \int_{2}^{4} \frac{1}{y} d x d y$$

Evaluate each iterated integral. (Many of these use results from Exercises 1-10 ).

$$\int_{1}^{2} \int_{4}^{9} \frac{3+5 y}{\sqrt{x}} d x d y$$

Evaluate each iterated integral. (Many of these use results from Exercises 1-10 ).

$$\int_{3}^{4} \int_{1}^{2}\left(\frac{6 x}{5}+\frac{y}{x}\right) d x d y$$

Evaluate each iterated integral. (Many of these use results from Exercises 1-10 ).

$$\int_{16}^{25} \int_{2}^{7} \frac{3+5 y}{\sqrt{x}} d y d x$$

Evaluate each iterated integral. (Many of these use results from Exercises 1-10 ).

$$\int_{0}^{3} \int_{4}^{5} x \sqrt{x^{2}+3 y} d y d x$$

Evaluate each iterated integral. (Many of these use results from Exercises 1-10 ).

$$\int_{3}^{9} \int_{5}^{7}\left(\frac{x}{y}+\frac{y}{5}\right) d x d y$$

Evaluate each iterated integral. (Many of these use results from Exercises 1-10 ).

$$\int_{0}^{3} \int_{1}^{2}\left(x y^{3}-x\right) d y d x$$

In Exercises $1-14,$ evaluate the iterated integral.

$$\int_{1}^{4} \int_{1}^{e} \frac{\ln x}{x y} d x d y$$

In Exercises $1-14,$ evaluate the iterated integral.

$$\int_{-1}^{0} \int_{-1}^{1}(x+y+1) d x d y$$

In Exercises $1-14,$ evaluate the iterated integral.

$$\int_{0}^{1} \int_{0}^{1}\left(1-\frac{x^{2}+y^{2}}{2}\right) d x d y$$

In Exercises $1-14,$ evaluate the iterated integral.

$$\int_{0}^{2} \int_{-1}^{1}(x-y) d y d x$$

In Exercises $1-14,$ evaluate the iterated integral.

$$\int_{0}^{3} \int_{-2}^{0}\left(x^{2} y-2 x y\right) d y d x$$

In Exercises $1-14,$ evaluate the iterated integral.

$$\int_{1}^{2} \int_{0}^{4} 2 x y d y d x$$

In Exercises $1-14,$ evaluate the iterated integral.

$$

\int_{0}^{1} \int_{1}^{2} x y e^{x} d y d x

$$

In Exercises $1-14,$ evaluate the iterated integral.

$$\int_{0}^{1} \int_{1}^{2} x y e^{x} d y d x$$

In Exercises $1-14,$ evaluate the iterated integral.

$$\int_{0}^{3} \int_{0}^{2}\left(4-y^{2}\right) d y d x$$

In Exercises $1-14,$ evaluate the iterated integral.

$$\int_{0}^{\ln 2} \int_{1}^{\ln 5} e^{2 x+y} d y d x$$

In Exercises $1-14,$ evaluate the iterated integral.

$$\int_{1}^{4} \int_{0}^{4}\left(\frac{x}{2}+\sqrt{y}\right) d x d y$$

Evaluate the integrals in Exercises $7-20$

$$

\int_{0}^{\sqrt{2}} \int_{0}^{3 y} \int_{x^{2}+3 y^{2}}^{8-x^{2}-y^{2}} d z d x d y

$$

In Exercises $1-14,$ evaluate the iterated integral.

$$

\int_{0}^{1} \int_{0}^{1} \frac{y}{1+x y} d x d y

$$

In Exercises $1-14,$ evaluate the iterated integral.

$$\int_{0}^{1} \int_{0}^{1} \frac{y}{1+x y} d x d y$$

In Exercises $1-14,$ evaluate the iterated integral.

$$\int_{-1}^{2} \int_{1}^{2} x \ln y d y d x$$

Evaluate the following iterated integrals.

$$\int_{0}^{1} \int_{0}^{1} x^{2} y^{2} e^{x^{3} y} d x d y$$

Evaluate the following iterated integrals.

$$\int_{1}^{2} \int_{1}^{2} \frac{x}{x+y} d y d x$$

In Exercises $1-14,$ evaluate the iterated integral.

$$\int_{\pi}^{2 \pi} \int_{0}^{\pi}(\sin x+\cos y) d x d y$$

Evaluate the following iterated integrals.

$$\int_{1}^{3} \int_{0}^{2} x^{2} y d x d y$$

Evaluate the following iterated integrals.

$$\int_{1}^{3} \int_{0}^{2} x^{2} y d x d y$$

Evaluate the following iterated integrals.

$$\int_{0}^{1} \int_{0}^{1} \frac{y}{1+x^{2}} d x d y$$

In the following exercises, evaluate the iterated integrals by choosing the order of integration.

$$\int_{1}^{e} \int_{1}^{e}\left(\frac{\ln y}{\sqrt{y}}+\frac{\ln x}{\sqrt{x}}\right) d y d x$$

In the following exercises, evaluate the iterated integrals by choosing the order of integration.

$$\int_{1}^{2} \int_{1}^{2}\left(\frac{\ln y}{x}+\frac{x}{2 y+1}\right) d y d x$$

Evaluate the iterated integral.

$$\int_{-1}^{0} \int_{-1}^{1}(x+y+1) d x d y$$

Evaluate the iterated integral.

$$\int_{1}^{4} \int_{1}^{e} \frac{\ln x}{x y} d x d y$$

In the following exercises, evaluate the iterated integrals by choosing the order of integration.

$$\int_{0}^{1} \int_{1}^{2} \frac{y}{x+y^{2}} d y d x$$

Evaluate the integrals in Exercises $7-20$

$$

\int_{0}^{1} \int_{0}^{2-x} \int_{0}^{2-x-y} d z d y d x

$$

Evaluate the following iterated integrals.

$$\int_{1}^{3} \int_{1}^{2}\left(y^{2}+y\right) d x d y$$

Evaluate the following iterated integrals.

$$\int_{1}^{3} \int_{1}^{2}\left(y^{2}+y\right) d x d y$$

Evaluate the following iterated integrals.

$$\int_{1}^{\ln 5} \int_{0}^{\ln 3} e^{x+y} d x d y$$

Evaluate the following iterated integrals.

$$\int_{1}^{\ln 5} \int_{0}^{\ln 3} e^{x+y} d x d y$$

In the following exercises, evaluate the iterated integrals by choosing the order of integration.

$$\int_{0}^{1} \int_{1}^{2} x e^{x+4 y} d y d x$$

In the following exercises, evaluate the iterated integrals by choosing the order of integration.

$$\int_{1}^{2} \int_{0}^{1} x e^{x-y} d y d x$$

In the following exercises, evaluate the iterated integrals by choosing the order of integration.

$$\int_{0}^{1} \int_{1}^{2}\left(\frac{x}{x^{2}+y^{2}}\right) d y d x$$

Evaluate the integrals in Exercises $7-20$

$$

\int_{-1}^{1} \int_{0}^{1} \int_{0}^{2}(x+y+z) d y d x d z

$$

Evaluate the integrals in Exercises $7-20$

$$

\int_{0}^{3} \int_{0}^{\sqrt{9-x^{2}}} \int_{0}^{\sqrt{9-x^{2}}} d z d y d x

$$

Evaluate the following iterated integrals.

$$\int_{0}^{2} \int_{0}^{1} 4 x y d x d y$$

Evaluate the following iterated integrals.

$$\int_{0}^{2} \int_{0}^{1} 4 x y d x d y$$

In Exercises $1-14,$ evaluate the iterated integral.

$$\int_{-1}^{2} \int_{0}^{\pi / 2} y \sin x d x d y$$

Evaluate the following iterated integrals.

$$\int_{0}^{2} \int_{0}^{1} x^{5} y^{2} e^{x^{3} y^{3}} d y d x$$

Evaluate the iterated integral.

$$\int_{0}^{1} \int_{1}^{2} x y e^{x} d y d x$$

In the following exercises, evaluate the iterated integrals by choosing the order of integration.

$$\int_{1}^{e} \int_{1}^{e}\left(\frac{x \ln y}{\sqrt{y}}+\frac{y \ln x}{\sqrt{x}}\right) d y d x$$

Evaluate the iterated integral.

$$\int_{0}^{1} \int_{0}^{1}\left(1-\frac{x^{2}+y^{2}}{2}\right) d x d y$$

Evaluate the integrals in Exercises $7-20$

$$

\int_{0}^{1} \int_{0}^{3-3 x} \int_{0}^{3-3 x-y} d z d y d x

$$

Evaluate the integrals in Exercises $7-20$

$$

\int_{0}^{1} \int_{0}^{1-x^{2}} \int_{3}^{4-x^{2}-y} x d z d y d x

$$

Evaluate the iterated integral.

$$\int_{0}^{2} \int_{-1}^{1}(x-y) d y d x$$

Calculate the iterated integral.

$\int_{1}^{3} \int_{1}^{5} \frac{\ln y}{x y} d y d x$

Evaluate the integrals in Exercises $7-20$

$$

\int_{0}^{2} \int_{-\sqrt{4-y^{2}}}^{\sqrt{4-y^{2}}} \int_{0}^{2 x+y} d z d x d y

$$

Evaluate the integrals in Exercises $7-20$

$$

\int_{0}^{1} \int_{0}^{1} \int_{0}^{1}\left(x^{2}+y^{2}+z^{2}\right) d z d y d x

$$

Evaluating integrals Evaluate the following integrals as they are written.

$$\int_{0}^{3} \int_{x^{2}}^{x+6}(x-1) d y d x$$

Evaluate the iterated integral.

$$\int_{0}^{3} \int_{0}^{2}\left(4-y^{2}\right) d y d x$$