
What is the integral of ?
Answer
444.6k+ views
Hint: In order to determine the integral of the given exponential function. In mathematics, an integral assigns numbers to functions in a way that describes displacement, area, volume, and other concepts that arise by combining infinitesimal data. The process of finding integrals is called integration.
Complete step by step solution:
We are given the exponential function is
Now, Let us consider,
Differentiating the exponential o ‘z’ with respect to ‘x’ , then
Comparing the exponential function with , so we can write
Since,
Now we can substitute the ‘dx’ and ‘z’ value into the given equation
We take the integral limit as to , we get
Expand the integral values on the exponential function, we can get
On compare the formula for indefinite integral with the above derivative equation, the
Where and are constant.
Hence, the integral of is .
Additional information:
In integral, there are two types of integrals in maths:
> Definite Integral
> Indefinite Integral
Definite Integral:
An integral that contains the upper and lower limits then it is a definite integral. On a real line, x is restricted to lie. Riemann Integral is the other name of the Definite Integral.
A definite Integral is represented as:
Indefinite Integral:
Indefinite integrals are defined without upper and lower limits. It is represented as:
Where C is any constant and the function is called the integrand.
Note:
We can derive the exponential function as follows
Let the
Differentiate with respect to x
We can change the denominator function as a numerator. So, it changed to negative exponential.
Complete step by step solution:
We are given the exponential function is
Now, Let us consider,
Differentiating the exponential o ‘z’ with respect to ‘x’ , then
Comparing the exponential function
Since,
Now we can substitute the ‘dx’ and ‘z’ value into the given equation
We take the integral limit as
Expand the integral values on the exponential function, we can get
On compare the formula for indefinite integral
Where
Hence, the integral of
Additional information:
In integral, there are two types of integrals in maths:
> Definite Integral
> Indefinite Integral
Definite Integral:
An integral that contains the upper and lower limits then it is a definite integral. On a real line, x is restricted to lie. Riemann Integral is the other name of the Definite Integral.
A definite Integral is represented as:
Indefinite integrals are defined without upper and lower limits. It is represented as:
Where C is any constant and the function
Note:
We can derive the exponential function
Let the
Differentiate with respect to x
We can change the denominator function as a numerator. So, it changed to negative exponential.
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