Maths 4.6Lesson outlineLesson 6 of 9 in Module 4
Integrals as Area
Read an integral as accumulated area, enough for densities and AUC.
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Learn
In this lesson11 parts
- 01Adding up under a curve
- 02Strips under x squared
- 03Area and the derivative
- 04Probability as area
- 05Checkpoint: integrals so far
- 06The ROC curve on the tiny ward
- 07AUC as a count of pairs
- 08The full ward
- 09What AUC does not say
- 10Integrals in Python
- 11Recap, challenge, and next: convexity
Key terms
The words this lesson introduces, each in one line. The module’s glossary collects them all.
- strip sum
- the total area of thin rectangles under a curve |
0.46875with four right-edge strips - integral
- the limit of the strip sums as the strips get thinner |
∫₀¹ x² dx = 1/3 - antiderivative
- a function whose derivative is the given function |
x³/3forx² - fundamental theorem of calculus
- the area's rate of growth is the curve's height |
A′(x) = x² - density
- a curve with total area 1, whose area over an interval is the probability of landing there |
2xon[0, 1] - ROC curve
- the true positive rate against the false positive rate as the threshold moves | the tiny ward's seven points
- AUC
- the area under the ROC curve |
0.7656on the tiny ward
Quiz
Your first pick on each question is the one that counts, and a right one earns a coin. Getting one wrong here is how the lesson sticks.