Application of Integrals Class 12 Maths Notes – Formulas & Quick Revision

Application of Integrals mein curves ke neeche area nikalna aata hai — diagram banao, integrate karo. Yahan aapko is chapter ke sabse important formulas aur quick revision points free milte hain — NCERT/CBSE syllabus ke hisaab se, boards aur JEE/NEET dono ke liye.

Important Formulas & Concepts — Application of Integrals

• Area under curve: A = ∫ₐᵇ y dx = ∫ₐᵇ f(x)dx
• y-axis ke saath: A = ∫ f(y)dy
• Circle x² + y² = a² ka area = πa² (verify by integration)
• Ellipse area = πab
• Two curves ke beech: ∫[f(x) − g(x)]dx (upper − lower)
• Intersection points limits dete hain
• Parabola-line, circle-line ke standard cases
• Symmetry use karke area × 2 ya × 4

Quick Revision Points

• Diagram banana COMPULSORY hai — bina diagram limits galat hongi
• Area hamesha positive — negative aaye to modulus lo
• x-axis ke neeche wala area alag se integrate karo
• Rationalised syllabus mein sirf standard curves ke areas hain
• Circle/ellipse/parabola ke areas symmetry se fast hote hain

FAQ

Limits kaise nikalti hain?

Curves ko simultaneously solve karke intersection points — wahi limits hain.

Ye chapter kitne marks ka?

4-6 marks — diagram + setup sahi to full marks pakke.

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