Show model answer and explanation
12
3x²=12.
Class 11 · English Version · Mathematics
Equations, patterns and functions
Differentiate polynomials and use a definite integral as accumulation.
About this lesson and its coverage
Original Kidemy Class 11 progression. This level has its own text, examples and questions. Curriculum versions share the progression; complete board-specific coverage still needs specification matching and additional material.
Learn the idea
A derivative gives local rate of change. Stationary points have zero derivative but need classification. A definite integral gives signed accumulation; area between a curve and axis may require splitting at roots.
Worked example
For y=x³−6x, y′=3x²−6. For y=3x², the integral of 3x² from 0 to 2 is [x³] from 0 to 2 = 8. Units of an integral combine the horizontal and vertical units.
- Identify the quantities and restrictions.
- Show a method with units or symbols.
- Check and explain the result.
Your written practice
Show your working on paper. Check your answer, then choose Next.
Show model answer and explanation
16
[x²]0 to 4=16.
Show model answer and explanation
5
2x−10=0.
Write in your own words. A guardian or teacher should review this response.
Show model answer and explanation
y″=2>0, so it is a local minimum at x=5.
Use curvature or derivative sign changes.
Write in your own words. A guardian or teacher should review this response.
Show model answer and explanation
The negative and positive signed parts cancel; areas counted positively are 1/2+1/2.
Distinguish signed accumulation from area.
Progress and browser storage
Notebook challenge, sources and further study
Apply the idea
Analyse a polynomial’s derivative and integral using a labelled sketch.
Review with a guardian or teacher
- Use the stated evidence or givens.
- Show reasoning rather than only a result.
- Review and explain one correction.
Keep your work on paper or in a local file. This page does not upload it or automatically grade the project.
Teacher-led lessons, schedules and prices for this outline are upcoming. You can use any starter practice above now without booking.
Your next step
Solo practice works without an account. Sign in to save a practice record to your learner profile.
Keep practising
Exact lesson links and related activities are labelled separately. Return-to-course links retain your selected learning path.