Integration fundamentals

What you'll learn

1. 1

   Integration is like adding up the area under a curve — imagine slicing a shape into thin strips and adding them up.

2. 2

   This curve shows y = x² from x=0 to x=2. The area under it is made of thin rectangles — the thinner they are, the more accurate the total.

3. 3

   Let's integrate y = 2x from x=0 to x=3. This is like finding the area of a triangle.

4. 4

   Drag the slider to see how more rectangles give a better estimate of the area under y = x² from x=0 to x=2.

5. 5

   What does integration find?

6. 6

   Now let's integrate y = x² from x=0 to x=2 using the power rule.

7. 7

   What is ∫₀² x² dx?