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Integrate the function $x\sqrt{9+x^2}$ from $-3$ to $3$

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Final Answer

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We can solve the integral $\int x\sqrt{9+x^2}dx$ by applying integration method of trigonometric substitution using the substitution

$x=3\tan\left(\theta \right)$

Learn how to solve definite integrals problems step by step online.

$x=3\tan\left(\theta \right)$

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Learn how to solve definite integrals problems step by step online. Integrate the function x(9+x^2)^1/2 from -3 to 3. We can solve the integral \int x\sqrt{9+x^2}dx by applying integration method of trigonometric substitution using the substitution. Now, in order to rewrite d\theta in terms of dx, we need to find the derivative of x. We need to calculate dx, we can do that by deriving the equation above. Substituting in the original integral, we get. Factor the polynomial 9+9\tan\left(\theta \right)^2 by it's greatest common factor (GCF): 9.

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Function Plot

Plotting: $x\sqrt{9+x^2}$

Main Topic: Definite Integrals

Given a function f(x) and the interval [a,b], the definite integral is equal to the area that is bounded by the graph of f(x), the x-axis and the vertical lines x=a and x=b

Used Formulas

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