Shaded Area and Integration Concepts

y = x + 2

y = x^3

y = x^2

y = 2x

Areas under curves are always larger.

Areas above curves are always smaller.

Areas under curves are below the axis, while areas above curves are above the axis.

There is no difference.

Find the midpoint of the curve.

Draw the curve again.

Integrate the function to find the area under the curve.

Calculate the area of the rectangle.

From 1 to 3

From 0 to 4

From 2 to 5

From 0 to 2

2

4

8

6

8

12

16

20

256/3 units squared

32 units squared

128/3 units squared

64 units squared

Addition

Multiplication

Subtraction

Division

128/3

64/3

32/3

16/3

To find the area of the rectangle.

To find the area under the curve.

To find the perimeter of the shape.

To find the shaded area above the curve.