In Exercises $27-30,$ integrate $f$ over the given curve. $$f(x, y)=x^{2}-y, \quad C : \quad x^{2}+y^{2}=4$ in the first quadrant from $(0,2)$ to $(\sqrt{2}, \sqrt{2})$$

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## Discussion

## Video Transcript

Oh, has function this to assign See to co sign t 40 from zero to well, your pie. So the march of the derivative would be too. Using the identity of the children is a function. We're the nine to go f oversee. Forget the data. We're gonna have zero to have high. I'm sorry. 0 to 1 0/4 Bi, You saw that? We have for sun t squared on this tickles nt Did she? Tom's too. So the answer is plying minus two minus to Times Square to

## Recommended Questions

In Exercises $27 - 30 ,$ integrate $f$ over the given curve.

$$

\begin{array} { l } { f ( x , y ) = x ^ { 2 } - y , \quad C : \quad x ^ { 2 } + y ^ { 2 } = 4 \text { in the first quadrant from } } \\ { ( 0,2 ) \text { to } ( \sqrt { 2 } , \sqrt { 2 } ) } \end{array}

$$

In Exercises $27 - 30$ , integrate $f$ over the given curve.

$$

\begin{array} { l } { f ( x , y ) = x + y , \quad C : \quad x ^ { 2 } + y ^ { 2 } = 4 \text { in the first quadrant from } } \\ { ( 2,0 ) \text { to } ( 0,2 ) } \end{array}

$$

In Exercises $27 - 30 ,$ integrate $f$ over the given curve.

$$

\begin{array} { l } { f ( x , y ) = \left( x + y ^ { 2 } \right) / \sqrt { 1 + x ^ { 2 } } , \quad C : \quad y = x ^ { 2 } / 2 \text { from } ( 1,1 / 2 ) \text { to } } \\ { ( 0,0 ) } \end{array}

$$

Integrate $f$ over the given curve.

$f(x, y)=x^{2}-y, \quad C: \quad x^{2}+y^{2}=4$ in the first quadrant from (0,2) to $(\sqrt{2}, \sqrt{2})$

In Exercises $27 - 30 ,$ integrate $f$ over the given curve.

$$f ( x , y ) = x ^ { 3 } / y , \quad C : \quad y = x ^ { 2 } / 2 , \quad 0 \leq x \leq 2$$

Integrate $f$ over the given curve.

$f(x, y)=x+y, \quad C: \quad x^{2}+y^{2}=4$ in the first quadrant from (2,0) to (0,2)

Integrate $f$ over the given curve.

$f(x, y)=\left(x+y^{2}\right) / \sqrt{1+x^{2}}, \quad C: \quad y=x^{2} / 2$ from $(1,1 / 2)$ to (0,0)

In exercises $27-32$, evaluate the iterated integral by converting to polar coordinates.

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

In Exercises $31-40,$ sketch the region of integration, reverse the order of integration, and evaluate the integral.

$$

\int_{0}^{2 \sqrt{\ln 3}} \int_{y / 2}^{\sqrt{\ln 3}} e^{x^{2}} d x d y

$$

In Exercises $29-32$ , find an equation for the level curve of the function $f(x, y)$ that passes through the given point.

$$

f(x, y)=\int_{x}^{y} \frac{d t}{1+t^{2}}, \quad(-\sqrt{2}, \sqrt{2})

$$