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