Area beneath a curve

In the picture

1. 11: the curved boundary line above
2. 22: the shaded region between the curve and the axis
3. 33: one thin vertical strip used to approximate area
4. 44: the horizontal axis segment under the shaded region

Examples

• Distance travelled over time from a speed curve
• Total water flow from a varying flow-rate curve

Quiz: Area beneath a curve (Age 17)

1. 1

   For a positive function, what does the definite integral over an interval represent?

   • The slope of the curve at one point in the interval
   • The maximum value of the function over the interval
   • The area between the curve and the horizontal axis over that interval
2. 2

   In the strip method, what is being added together to approximate the area under a curve?

   • The lengths of small pieces of the curve
   • The slopes of tangent lines along the curve
   • The areas of thin vertical rectangular strips
3. 3

   What happens to the approximation of the area as the vertical strips are made narrower and more numerous?

   • It becomes less accurate because there are more pieces
   • It approaches the exact value of the integral
   • It remains unchanged no matter how narrow the strips are

The answers, each with its explanation, are in the app. This lesson has left the free week, so its quiz is part of the subscription.