Evaluate the integral

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


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

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{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}


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Learn more about this topic:

Evaluating Definite Integrals Using the Fundamental Theorem


Chapter 16 / Lesson 2

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.

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