Find the integral: integral of (x^3)(x^2 + 9)^(1/2) dx.

Question:

Find the integral:

$$\int x^{3}(x^{2}+9)^{1/2}\ dx $$

Substitution Method:

The method of finding the integral by substitution of a new variable in the place of some function and the other function is divisible by the derivative of the substituted function is known as the substitution method.

Answer and Explanation: 1

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Given:

$$I=\int x^{3}(x^{2}+9)^{d\frac{1}{2}}\text{ d}x $$

Let {eq}x^{2}+9=t {/eq} and differentiate with respect to {eq}x. {/eq}

$$\begin{align...

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Evaluating Definite Integrals Using the Fundamental Theorem

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Chapter 16 / Lesson 2
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The fundamental theorem of calculus makes finding your definite integral almost a piece of cake. See how the definite integral becomes a subtraction problem after applying the fundamental theorem of calculus.


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