# Evaluate the definite integral: {eq}\displaystyle \int_0^1 3 \sqrt {(1 + 7x)} \ dx {/eq}.

## Question:

Evaluate the definite integral:

{eq}\displaystyle \int_0^1 3 \sqrt {(1 + 7x)} \ dx {/eq}.

## Definite Integral:

The integral in which the value of the limit is given is known as the definite integral. The value of this type of integral is fixed that's why we do not add constant C after integrating this type of integral.

Become a Study.com member to unlock this answer!

Given:

$$I=\int_{0}^{1}3\sqrt{1+7x}\text{ d}x$$

Let {eq}1+7x=t {/eq} and differentiate with respect to {eq}x. {/eq}

\begin{align} 7&=\dfrac{...

Evaluating Definite Integrals Using the Fundamental Theorem

from

Chapter 16 / Lesson 2
1.2K

In calculus, the fundamental theorem is an essential tool that helps explain the relationship between integration and differentiation. Learn about evaluating definite integrals using the fundamental theorem, and work examples to gain understanding.