Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 month ago

# why do integrals always have dx next to them?

What does it mean????

Relevance
• Becaause if there are several 'unknowns' in the integral, the 'dx' indicates which unknown is to be integrated.

e.g. Int(x + a) dx

• Not always but mostly. That means with respect to x.

In u substitution method it's in du, which means with respect to u.

• The dx tells you that you are integrating with respect to x. Sometimes it might be dy or dz or d(theta) or several of them.

For example, when you take the derivative of y = x^3 , you get dy = 3x^2 dx

This is the dx that appears in the integral. It means the differential of x.

• Normally ydx is the area of a rectangle with height y and width. Integral is the total area. Let a and b be limits. This interval is divided in to 10 parts with equal intervals. The total area will be

y1 dx+y2 dx+y3 dx +.... This sum when dx is very small can be written as ydx integrated between the limits a and b. Therefore dx always comes.