[Solved] What is the Integral of 1? | Integration of 1

The integral of 1 is equal to x+C where C is a constant. The integration of 1 is denoted by ∫1 dx, and its formula is given as follows:

∫1 dx = x+C

where C is an arbitrary integration constant. Here we will learn how to integrate 1.

Integration of 1

Question: What is the integration of 1?

Solution:

As 1 can be written as 1=x⁰, the integration of 1 is given by

∫1 dx = ∫x⁰ dx +C where C is a constant.

⇒ ∫1 dx = $\dfrac{x^{0+1}}{0+1}$ +C

⇒ ∫1 dx = $\dfrac{x^{1}}{1}$ +C

⇒ ∫1 dx = x +C.

So the integration of 1 is equal to x+C, and this is obtained by the power rule of integration.

Related Topics: Integral of 0 (zero)

Integration of 1/2x

Definite Integral of 1

Question: Find the definite integral of 1 from -1 to 1, that is, Find ∫-11 1 dx.

Answer

From above, we know that the integral of 1 is a constant x+C. Thus,

$\int 1 \ dx$ $=\Big[x+C \Big]_{-1}^1$

= (1+C) – (-1+C)

= 1+1

= 2.

So the definite integration of 1 from -1 to 1 is equal to 2.

Read Also: How to integrate ln(x)

FAQs