Integration Formulas for Class 12 Maths | Maharashtra Board
If you are a Maharashtra Board Class 12 student, understanding Integration (समाकलन) is a key part of your Mathematics syllabus. It's not just about memorizing formulas; it's about knowing how to find the integral of a function, which is the reverse process of differentiation. This page explains the core concepts directly, as they are presented in your textbooks.
What is Integration in Class 12 Maths?
In simple terms, integration is the process of finding a function whose derivative is given. If differentiation breaks a function down into smaller parts (like finding the rate of change), integration puts those parts together to find the whole. The symbol for integration is ∫. The function to be integrated is called the integrand.
Why is This Topic Important for Your Exams?
Integration forms the basis for many advanced topics in mathematics and its applications in physics, economics, and engineering. For your HSC board exams, questions from this chapter carry significant weightage. Mastering the standard formulas and methods is essential for solving problems in Application of Integrals (for finding areas) and in the Differential Equations chapter that follows.
Here, you will find a structured list of resources and explanations related to the Class 12 Mathematics curriculum of the Maharashtra State Board. Use the links below to navigate to specific topics or related chapters to build a strong foundation.
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Select a subject from the options below to access Maharashtra Board Class 12th books for that specific subject. Each subject page contains all available books and study materials.
Aarogy Va Shaareerik Shikshan (आरॊग्य व शारीरिक शिक्षण)
Agriculture Science And Technology
Animal Science And Technology
Aventuras - Part - 2 (Spanish)
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Book - Keeping And Accountancy
Chemistry
Child Development
Child development (बाल विकास)
Chinese Language
Co-operation
Cooperation (सहकार)
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English Yuvakbharati
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Food Science And Technology
French Rencontres Part - 2
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Geography (भूगोल)
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Haru - 2
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Logic
Maths And Statistics (Arts And Science) Part - I
Maths and Statistics (Arts and Science) Part - II
Maths and Statistics (Commerce) Part - I
Maths and Statistics (Commerce) Part - II
Organisation of Commerce And Management
Palippakaso (पालिप्पकासो)
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Sanskrit Alhad (संस्कृत आल्हाद)
Secretarial Practice
Sociology
Sociology (समाजशास्त्र)
Sprachlotsen 2 (German Coursebook)
Tarkshastra (तर्कशास्त्र)
Textiles
Vastrashaastr (वस्त्रशास्त्र)
Yuvak Bharati
Yuvak Bharati (युवकभारती )
Yuvakbharati (युवकभारती)
Дружба Druzhba (Friendship) Part II (Russian Language)
अन्नविज्ञान आणि तंत्रज्ञान
अर्थशास्त्र
अर्धमागधी प्राकृत
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कलेचा इतिहास व रसग्रहण
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गणित कला-विज्ञान भा-१
गणित कला-विज्ञान भा-२
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गुल-हाय-फारसी
गृहव्यवस्थापन
ग्रंथालय व माहितीशास्त्र
चिटणिसाची कार्यपध्दती
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हिदायतुल अरबियाह
Standard Integration Formulas for Maharashtra Board Class 12
Here are the fundamental formulas you need to know. These are directly applicable to your textbook problems and exam questions.
1. Basic Integration Formulas (मुलभूत समाकलन सूत्रे)
These are derived directly from the derivatives you learned in Class 11.
- ∫ xn dx = (xn+1)/(n+1) + C, where n ≠ -1
- ∫ 1/x dx = log |x| + C
- ∫ ex dx = ex + C
- ∫ ax dx = (ax)/log a + C (a > 0, a ≠ 1)
- ∫ sin x dx = -cos x + C
- ∫ cos x dx = sin x + C
- ∫ sec2 x dx = tan x + C
- ∫ cosec2 x dx = -cot x + C
- ∫ sec x tan x dx = sec x + C
- ∫ cosec x cot x dx = -cosec x + C
- ∫ 1/(√(1-x2)) dx = sin-1 x + C
- ∫ 1/(1+x2) dx = tan-1 x + C
- ∫ 1/(|x|√(x2-1)) dx = sec-1 x + C
2. Methods of Integration (समाकलनाची पद्धती)
Direct formulas are not enough for all functions. You need to learn these methods.
Integration by Substitution (प्रतिस्थापन पद्धत)
This method is used when a function can be converted into a standard form by substituting a part of it with a new variable. For example, to find ∫ sin(ax+b) dx, you substitute t = ax+b.
Integration by Parts (भागाकार पद्धत)
This is based on the product rule of differentiation. The formula is: ∫ u v dx = u ∫ v dx - ∫ [u' ∫ v dx] dx. A common way to remember it is: ∫ (First Function) * (Second Function) dx. Choosing the
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