Math 252 Calculus III: Double Integration z

x

y

by: javier

main idea

main idea area of a triangle 3 different ways

area of a triangle 3 different ways Suppose we wanted to find the area under the curve. 6

f(x) = 3 − x

4

2

0 −4

−2

0

z

2

4

area of a triangle 3 different ways Suppose we wanted to find the area under the curve. by Middle School Methods 6

f(x) = 3 − x

4

2

0 −4

−2

0

z

2

4

area of a triangle 3 different ways Suppose we wanted to find the area under the curve. by Calc I Methods 6

f(x) = 3 − x

4

2

0 −4

−2

0

z

2

4

area of a triangle 3 different ways Suppose we wanted to find the area under the curve. by Calc III Methods 6

f(x) = 3 − x

4

2

0 −4

−2

0

z

2

4

area of a triangle 3 different ways Suppose we wanted to find the area under the curve. 1.2 f(x) = sin(x)

1 0.8 0.6 0.4 0.2 0 −1

0

1

2

z

3

4

area of a triangle 3 different ways Suppose we wanted to find the area under the curve. by Middle School Methods 1.2 f(x) = sin(x)

1 0.8 0.6 0.4 0.2 0 −1

0

1

2

z

3

4

area of a triangle 3 different ways Suppose we wanted to find the area under the curve. by Calc I Methods 1.2 f(x) = sin(x)

1 0.8 0.6 0.4 0.2 0 −1

0

1

2

z

3

4

area of a triangle 3 different ways Suppose we wanted to find the area under the curve. by Calc III Methods 1.2 f(x) = sin(x)

1 0.8 0.6 0.4 0.2 0 −1

0

1

2

z

3

4

area of a triangle 3 different ways Suppose we wanted to find the area under the curve. 1.2 1 2

f(x) =

0.8

/2 e−x √ 2

0.6 0.4 0.2 0 −3

−2

−1

0

z

1

2

3

area of a triangle 3 different ways Suppose we wanted to find the area under the curve. by Middle School Methods 1.2 1 2

f(x) =

0.8

/2 e−x √ 2

0.6 0.4 0.2 0 −3

−2

−1

0

z

1

2

3

area of a triangle 3 different ways Suppose we wanted to find the area under the curve. by Calc I Methods 1.2 1 2

f(x) =

0.8

/2 e−x √ 2

0.6 0.4 0.2 0 −3

−2

−1

0

z

1

2

3

area of a triangle 3 different ways Suppose we wanted to find the area under the curve. by Calc III Methods 1.2 1 2

f(x) =

0.8

/2 e−x √ 2

0.6 0.4 0.2 0 −3

−2

−1

0

z

1

2

3