Question

Write in a short form as an indefinite integral and indicate the integrand and the variable of integration. The derivate of what function is x^2 + 4x.​

Answer 1

Answer:

$\frac{x^3}{3}+2x^2 + K$

Step-by-step explanation:

We can equate the expression x^2+4x to f(x) and specify the variable of integration , the integrand and the symbol simply like this ,

Let,

$f(x)=x^2+4x\\\\F'(x)=f(x)\\\\\int f(x)\ dx=F(x) + K$

Where the integrand is f(x) , x is the variable of integration , c is the constant of integration , and ∫ is the symbol of integration.

The derivate of what function is x^2 + 4x?

To find that out we integrate the function because Integrating a differentiate is the process of obtaining the original process because Integrals are also called as Anti-derivatives.

So,

$\int\ x^2+4x \ dx$

This is an indefinite integral which would result in an addition of a constant later on because it does not have limits. The variable of integration is x because there is only one variable present in this expression so naturally the variable of concern is x

so now we solve,

$\int\ x^2+4x \ dx\\\\\frac{x^3}{3}+4(\frac{x^2}{2}) + K\\\\\frac{x^3}{3}+2x^2 + K$

Where K is the constant of the indefinite integral.