7. Integrals

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Integrals Class 12 Maths

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Summary:

Integration is the inverse process of differentiation. In the differential calculus, we are given a function and we have to find the derivative or differential of this function, but in the integral calculus, we are to find a function whose differential is given. Thus, integration is a process which is the inverse of differentiation.

Let $$\frac{d}{dx}F(x) = f(x)$$. Then, we write $$\int{f(x) dx} = F(x) + C$$. These integrals are called indefinite integrals or general integrals, C is called constant of integration. All these integrals differ by a constant.

From the geometric point of view, an indefinite integral is collection of family of curves, each of which is obtained by translating one of the curves parallel to itself upwards or downwards along the y-axis.