Application of Definite Integration — Class 12 Maharashtra HSC Mathematics revision notes
A 5-page visual revision sheet for Application of Definite Integration, written for Class 12 Maharashtra HSC Mathematics. Formulas, diagrams and the traps that cost marks, laid out to be read the night before rather than the term before. Free, and it opens inside CapCompass.
What this Application of Definite Integration sheet covers
- Area Under a Curve
- Area with vertical strips (dx) and horizontal strips (dy)
- region bounded by y=f(x), the X-axis, x=a and x=b, with f(x)>=0
- region bounded by x=g(y), the Y-axis, y=c and y=d, with g(y)>=0
- Area under a curve, dx strips
- Area under a curve, dy strips
- A Curve That Crosses the X-axis
- Area when the curve crosses the axis
- Area Between Two Curves
- let A1 be the area under y=f(x) and A2 the area under y=g(x), both from x=a to x=b
- Setting up the area between two curves
- Area between a line and a parabola
- Setting up the integral correctly
- Symmetry shortcuts
- curve symmetric about the Y-axis, region spanning x=-a to x=a
- curve symmetric about the X-axis, region spanning y=-b to y=b
- Common enclosed shapes and their setup
- Circle
- Ellipse
- Parabola and a line
- Two intersecting parabolas
- Area of a circle by integration
- Traps that cost marks
- Tricks that save time
How CapCompass uses this sheet
These notes are not a standalone PDF. CapCompass plans Mathematics chapter by chapter against your real exam dates and free hours, and when the plan reaches Application of Definite Integration the sheet opens inside the study block itself — at the page covering the sub-topic that block is on, with the timer still running. Revision arrives at the moment the plan says revise, instead of having to be gone looking for.