Integrals Class 12 Notes Chapter 7

Integrals

Integration is referred to the process which is inverse to that of differentiation. In the integration, we will be responsible for finding the function whose differential is provided to us. Integrals are the functions which satisfy a given differential equation.

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CBSE Class 12 Maths Notes Chapter 7 Integrals – Related Links

• Integration
• Indefinite Integrals
• Application of Integrals
• Integrals For Class 12
• Application of Integrals for Class 12
• Integral Calculus

What are Indefinite Integrals?

If integration is inverse of differentiation, then

Properties of Indefinite Integrals

Integrals follow certain properties as follows:

• \(\begin{array}{l}\int [f(x)+g(x)dx]=\int f(x)dx+\int g(x)dx\end{array} \)
• For any given real number r,
  \(\begin{array}{l}\int r f(x)dx]=r\int f(x)dx\end{array} \)
• If f₁, f₂, f₃ … are the functions and r₁,r₂,r₃… are the designated real numbers. Then,

Integration using Partial Fractions

The rational function property can be seen in fractions and is followed by the ratio of two polynomials such as R(x)/S(x) where x and S(x)

Integration using Substitution

In this method, we change the variable of another variable in order to reduce the integral into fundamental integrals. We can get some standard integrals as the following.

• \(\begin{array}{l}\int tan x dx=log\left | secx \right |+C\end{array} \)
• \(\begin{array}{l}\int cot x dx=log\left | sinx \right |+C\end{array} \)
• \(\begin{array}{l}\int sec x dx=log\left | sec x + tan x\right |+C\end{array} \)
• \(\begin{array}{l}\int cosec x dx=log\left | cosec x – cot x\right |+C\end{array} \)

Important Questions:

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