Class 12 Mathematics — Chapter 1: INTEGRALS

What you'll learn

• ▸Integration as the Inverse Process of Differentiation
• ▸The Constant of Integration (C)
• ▸Notation and Terminology of Indefinite Integrals
• ▸Standard Integration Formulas
• ▸Properties of Indefinite Integrals
• ▸Integration by Method of Inspection

Chapter Summary

--- PAGE 1 --- 12080CH07 Chapter 7 INTEGRALS ✧ *Just as a mountaineer climbs a mountain – because it is there, so* *a good mathematics student studies new material because* *it is there. — JAMES B. BRISTOL* ✧ 7.1 Introduction Differential Calculus is centred on the concept of the derivative. The original motivation for the derivative was the problem of defining tangent lines to the graphs of functions and calculating the slope of such lines. Integral Calculus is motivated by the problem of defining and calculating the area of the region bounded by the graph of the functions. If a function f is differentiable in an interval I, i.e., its derivative f ' exists at each point of I, then a natural question arises that given f ' at each point of I, can we determine the function? The functions that could possibly have given function as a derivative are called anti derivatives (or primitive) of the function. Further, the formula that gives all these anti derivatives is called the **…

Practice Questions from this Chapter

Tap "Get Solution" on any question to ask our AI tutor.

1. Calculate curve areas simply? Get Solution →
2. Explain anti-differentiation clearly? Get Solution →
3. Apply integration in physics? Get Solution →
4. According to the text, Integral Calculus is motivated by the problem of defining and calculating what? Get Solution →
5. What is another term for an 'anti derivative' of a function? Get Solution →
6. In the expression ∫ f(x) dx, what is the function f(x) called? Get Solution →
7. What is the process of finding an anti derivative called? Get Solution →
8. What is the indefinite integral of cos x? Get Solution →

Did you know?

• 💡 The integral symbol ∫ is an elongated S, representing the concept of sum.
• 💡 Calculus, including integration, was independently invented by Newton and Leibniz.
• 💡 Integration helps GPS devices calculate exact positions from velocity data.
• 💡 Architects use integration to determine the volume of complex building designs.
• 💡 Ancient mathematicians like Archimedes used methods similar to integration for areas.

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