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.
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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)
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
Q1: What is the integral of 1?
Answer: The integral of the constant 1 is ∫1 dx = x+C, C is any constant.
Q2: What is ∫1 dx?
Answer: ∫1 dx is equal to x+C where C is a constant.