General ScienceMadrid 2026Question 2A
X-linked inheritance
A healthy father and a carrier mother: the Punnett square and why it comes out this way
12 chapters · 9 minWatch the lesson →
9 chapters · 8 min · Synthetic voices · Press ▶ to startReport a mistakeOpen full screen ↗
Problem statement
(2 marks) Let $f(x) = \ln(x)$. Find the area of the region enclosed by the graph of $f(x)$, the x-axis and the line $x = e$.
Source: Madrid university entrance exam (PAU, Spain) · 2025-2026 · Ordinary session · Mathematics · Question 5.1. Official exam set by the public universities of the Community of Madrid, to whom it belongs; translated from Spanish and reproduced with its source in order to explain it for teaching purposes.What this lesson answers
- What region is it, and how big can it be?
- Why does the integral go from 1 to e?
- Why by parts, and why u = ln x?
- Why is the area a subtraction of two values?
- Another route: integrating in y, without parts
- The answer and how to check it
- Common mistakes to avoid
- Exam tips
- If you want full marks
More lessons
General ScienceMadrid 2026Question 3A
A geostationary satellite
The four forces, the gravity that makes it orbit and the angular velocity: why it is solved this way
11 chapters · 9 minWatch the lesson →
General ScienceMadrid 2026Question 3B
A box pushed against friction
Free-body diagram, friction, net force and braking: why it is solved this way
12 chapters · 9 minWatch the lesson →
Was it useful?
Tell me which problem you would like to see explained like this, or if you have found a mistake, and I will let you know when there are new lessons.