FUZY MATH ACADEMY

CBSE Class 12 Result 2026 Expected Soon Student of FM Academy The Central Board of Secondary Education (CBSE) is likely  to announce the Class 12 Results 2026 in third week of May 2026. According to recent reports and DigiLocker updates, the result preparation process is almost complete and it may be published soon. Students are advised to keep their roll number and admit card ready for quick access to results. How and Where to Check CBSE Class 12 Result 2026 Students can check their results on these official platforms: CBSE Official Website DigiLocker SMS Service UMANG App The digital marksheet will also be available. Useful official websites: CBSE Official Website CBSE Results Portal DigiLocker CBSE Class 12 Passing Criteria 2026  CBSE students must score at least 33% marks to pass. Important Rules Minimum 33% marks in each subject Separate passing required in theory and practical exams Internal assessment must also be cleared Students failing in one subject may get compartm...

Class 12 Maths Chapter 7 Integrals – Exercise 7.11 NCERT Solutions Introduction Exercise 7.11 focuses on applications of definite integrals in finding areas. Students learn how to calculate areas bounded by curves, coordinate axes, and lines using integration. This exercise is crucial for connecting calculus with geometry and practical applications. Key Formulas Area under curve y = f ( x ) from x = a to x = b : Area = ∫ a b f ( x )   d x Area between two curves y = f ( x ) and y = g ( x ) : Area = ∫ a b [ f ( x ) − g ( x ) ]   d x where  f ( x ) ≥ g ( x ) Area bounded by curve and y‑axis: Area = ∫ c d x   d y Common Mistakes Forgetting to take absolute value when curve lies below x‑axis. Incorrectly identifying limits of integration. Mixing up which curve is above the other. Arithmetic errors in evaluating definite integrals. NCERT Questions with Step‑by‑Step Solutions (10) Q1. Find area under curve y = x 2 from x = 0 to x = 3 . Area = ∫ 0 3 x 2 d x = [ x 3 3 ] 0 3 = 9 Q2. Fi...

Class 12 Maths Chapter 7 Integrals – Exercise 7.10 NCERT Solutions Introduction Exercise 7.10 focuses on definite integrals and applications of properties. Students practice evaluating integrals using symmetry, periodicity, and transformations. This exercise strengthens problem‑solving skills and prepares students for advanced calculus and competitive exams. Key Properties Recap Symmetry Property: ∫ a b f ( x )   d x = ∫ a b f ( a + b − x )   d x Reversal of Limits: ∫ a b f ( x )   d x = − ∫ b a f ( x )   d x Splitting Interval: ∫ a b f ( x )   d x = ∫ a c f ( x )   d x + ∫ c b f ( x )   d x Common Mistakes Forgetting to apply symmetry correctly. Confusing periodic functions with symmetric ones. Arithmetic errors in trigonometric integrals. Not checking which function is dominant in area problems. NCERT Questions with Step‑by‑Step Solutions (10) Q1. Evaluate ∫ 0 π x sin ⁡ x 1 + cos ⁡ 2 x   d x . Using property: I = ∫ 0 π x sin ⁡ x 1 + cos ⁡ 2 x   d x = π 2 ∫ 0 π sin ⁡ x 1 + cos ⁡ 2 ...

Class 12 Maths Chapter 7 Integrals – Exercise 7.9 NCERT Solutions Introduction Exercise 7.9 focuses on definite integrals and their properties. Students learn how to apply properties of definite integrals to simplify calculations and solve problems efficiently. This exercise is important for mastering advanced integration techniques and preparing for competitive exams. Key Properties of Definite Integrals Property 1: ∫ a b f ( x )   d x = ∫ a b f ( t )   d t Property 2: ∫ a b f ( x )   d x = − ∫ b a f ( x )   d x Property 3: ∫ a b f ( x )   d x = ∫ a c f ( x )   d x + ∫ c b f ( x )   d x Property 4: ∫ a b f ( x )   d x = ∫ a b f ( a + b − x )   d x Common Mistakes Forgetting to apply symmetry property correctly. Confusing limits when reversing integration. Arithmetic errors in splitting integrals. Misidentifying the function transformation in property 4. NCERT Questions with Step‑by‑Step Solutions (10) Q1. Evaluate ∫ 0 1 ( x 2 + ( 1 − x ) 2 )   d x . Using property 4: ∫ 0 1 f ( x ) ...

Class 12 Maths Chapter 7 Integrals – Exercise 7.8 NCERT Solutions Introduction Exercise 7.8 focuses on definite integrals as areas under curves. Students learn how to apply integration to calculate areas bounded by curves, coordinate axes, and lines. This exercise is crucial for connecting integration with geometry and real‑life applications. Key Formulas Definite Integral as Area: Area = ∫ a b f ( x )   d x Area between Curve and x‑axis: Area = ∫ a b ∣ f ( x ) ∣   d x Area between Two Curves: Area = ∫ a b [ f ( x ) − g ( x ) ]   d x where f ( x ) ≥ g ( x ) in [ a , b ] . Common Mistakes Forgetting to take absolute value when curve lies below x‑axis. Incorrectly identifying limits of integration. Mixing up which curve is on top when finding area between two curves. Arithmetic errors in evaluating definite integrals. NCERT Questions with Step‑by‑Step Solutions (10) Q1. Find area under curve y = x 2 from x = 0 to x = 2 . Area = ∫ 0 2 x 2 d x = [ x 3 3 ] 0 2 = 8 3 Q2. Find area under c...