Maths · Class 12 · Chapter 8
Application of Integrals
7 lessons 61 min 2 simulations
School geometry has formulas for triangles, rectangles and circles, but not for a region with a curved edge. This chapter uses the definite integral to measure such regions. A region is cut into thin strips, vertical or horizontal, their areas are added, and the sum becomes an integral. The same idea gives the area of a circle and an ellipse, handles parts of a curve that dip below the axis, and, as a JEE extension, the area between two curves.
What the exam asks
Area questions in JEE Main usually take one of a few forms: a region under a curve, a region cut from a circle, ellipse or parabola, or the area between a line and a parabola. Most marks are lost in the set-up, not the integration: drawing the region wrongly, choosing strips that need two integrals when one would do, missing an intersection point, or adding a negative piece as if it were positive. Sketch first, find the intersections, then choose the strip.
Lessons
7 lessons · 61 min
1Area from thin stripsNCERT §8.1–8.210 min 1 sim2Horizontal stripsNCERT §8.27 min3Regions below the x-axisNCERT §8.2 (Remark), Misc. Examples11 min 1 sim4Circles and ellipsesNCERT §8.2 (Examples 1–2)7 min5Parabolas and symmetryNCERT §8.1–8.2 (standard forms)7 min6Area between two curvesNCERT §8.2 onwards, JEE extension (not in the rationalised text)8 min7Chapter reviewMust-know facts, traps and formulas11 min