Evaluate the integral \int_0^2 \frac{24}{x^2 + 4} \,dx

Question:

Evaluate the integral {eq}\int_0^2 \frac{24}{x^2 + 4} \,dx {/eq}

Integration by Substtution

Evaluating some integrals substitution method is very helpful to make the integrals easier. A suitable portion of the integrand is generally substituted by a variable and the differential coefficient of the substituted variable with respect to the original variable is calculated to substitute the differential also. The variable is substituted back after integration.

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We have to evaluate the integral {eq}\int_0^2\frac{24}{x^2+4}dx {/eq}.

Let us substitute {eq}x=2\tan \theta {/eq}

Differentiating we get

{eq}\beg...

Evaluating Definite Integrals Using the Fundamental Theorem

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Chapter 16 / Lesson 2
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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.