# >> College & Higher Education >> Technical Schools

How to Find the Exact Area Under a Curve

A common application of calculus integrals is solving for the area under a given function that describes a curve. In every calculus course, you can expect to see this problem as it is a basic lesson which leads to more interesting problems, such as finding the area between two curves and later on, finding the volume of a shape created in three dimensions as described by a two dimension function. Once you master this fundamental rule, the other rules can be mastered.

Instructions

- 1
  Start with a curve described by the function is y = x^3 + 4x + 2 and solve for the area between x coordinates 0 and 2.
- 2
  Integrate the function x^3 + 4x + 2 using the standard integration formula, which is the integral of x^n = (1/n+1)(x^n+1). Thus, our integral result is (1/4)x^4 + 2x^2 + 2x.
- 3
  Insert the values 0 and 2 into the integrated function (1/4)x^4 + 2x^2 + 2x and subtract the value computed by 0 from the value computed by 2. Using 0, the function evaluates simply to 0. Using 2, the function evaluates to (1/4)16 + 2(4) + 4 = 4 + 8 + 4 = 16. 16 - 0 = 16, which is our solution.

How to Find the Resistance of a Capacitor

Technical Schools for Construction in Miami, Florida