Question

What is the geometrical interpretation of indefinite integral?

• A. The equation $\int f\left(x\right)dx=F\left(x\right)+C$, represents a family of curves.
• B. The different values of $C$ will correspond to different members of this family.
• C. These members cannot be obtained by shifting any one of the curves parallel to itself.
• D. None of these

Answer 1

Answer: (A), (B)

The equation $\int f\left(x\right)dx=F\left(x\right)+C$, represents a family of curves.
The different values of $C$ will correspond to different members of this family.

$\int f\left(x\right)dx=F\left(x\right)+C$ represents a family of curves and different values of $C$ corresponds to different members of this family.

These members can be obtained by shifting any one of the curves parallel to itself.

Above statement can be considered as geometrical representation of indefinite integral

Therefore options $A$ and $B$ are correct