Integrate the given function \int^5_4 \frac{2s ds}{(s-3)^3}

Question:

Integrate the given function {eq}\displaystyle \int^5_4 \frac{2s \: ds}{(s-3)^3} {/eq}

Definite Integrals:

Calculus is defined to have two fundamental theorems. The second fundamental theorem of calculus concerns the definition of a definite integral's solution. If the definite integral is defined with an upper and lower bound of {eq}\displaystyle a {/eq} and {eq}\displaystyle b {/eq}, then the definite integral's answer is:

{eq}\displaystyle \int_{a}^{b} f(x)dx= F(b)-F(a) {/eq}.

Answer and Explanation: 1

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We are asked to integrate the given function. To do so, we need to apply the u-substitution by letting {eq}u= s-3 {/eq}, {eq}s=u+3 {/eq} and {eq}du=...

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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.


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