Question

In Exercises 3-8, evaluate the definite integral by the limit definition. $$ \int_{4}^{10} 6 d x $$

Short answer

The value of the definite integral \( \int_{4}^{10} 6 dx \) is 36.

Step-by-step solution

Understanding the integral

We are required to evaluate the definite integral \( \int_{4}^{10} 6 dx \). This implies the integral of a constant \(6\) from \(x = 4\) to \(x = 10\). The integral of a constant is simply the constant multiplied by the variable.

Setting up the integral

From the definition, a definite integral of a function can be considered as the limit of a Riemann sum. This particular integral, however, is quite simple since the function being integrated is a constant. This makes it very straightforward to set up the integral:

Evaluating the integral

The integral \( \int_{4}^{10} 6 dx \) is equal to \( 6 * (10 - 4) = 6 * 6 = 36 \).