Evaluate the integral

{eq}\int^x_0 \sqrt {t + 3} dt. {/eq}

Question:

Evaluate the integral

{eq}\int^x_0 \sqrt {t + 3} dt. {/eq}

Definite Integral:

Definite Integrals are those integrals which do contain upper and lower limit. There is no integration constant in the definite integral. To evaluate the definite integral, we must first integrate it simply considering it as the antiderivative and then apply the limits to find out the final result.

Reverse power rule of integration is used to find out the integral of the form {eq}x^n. {/eq} It can be given by the following formula:

{eq}\int x^n \ dx = \frac {x^{n+1}}{n+1} + C \\ {/eq}

where C is the constant of integration.

Answer and Explanation: 1

Become a Study.com member to unlock this answer!

View this answer

Given:

{eq}\int^x_0 \sqrt {t + 3} dt \\ {/eq}

On rewriting the above integral, we get:

{eq}\int^x_0 (t + 3)^{\frac {1}{2}} \ dt \\ {/eq}

On...

See full answer below.


Learn more about this topic:

Loading...
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.


Related to this Question

Explore our homework questions and answers library