- #1

darkchild

- 155

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## Homework Statement

[tex]\int_{-3}^{1}\frac{x}{\sqrt{9-x^{2}}}[/tex]

## Homework Equations

Let f be continuous on the half-open interval (a, b] and suppose that

[tex] \lim_{x \to a^{+}} |f(x)| = \infty[/tex]. Then

[tex]\int_{a}^{b}f(x) dx = \lim_{ t \to a^{+}}\int_{t}^{b}f(x)

dx[/tex]

## The Attempt at a Solution

[tex]\int_{-3}^{1}\frac{x}{\sqrt{9-x^{2}}}

= \lim_{ t \to -3^{+}}\int_{t}^{1}\frac{x}{\sqrt{9-x^{2}}}

[/tex]

[tex] u = 9 - x^{2} [/tex]

[tex] du = -2x dx [/tex]

[tex] \lim_{ t \to -3^{+}}\int_{t}^{1}\frac{x}{\sqrt{9-x^{2}}}

= \lim_{ t \to 0^{+}}-\frac{1}{2}\int_{t}^{8} u^{-1/2} du

=\lim_{ t \to 0^{+}}-u^{1/2}|_{t}^{8}

=-\sqrt{3sin(1)} + \lim_{ t \to -3^{+}}\sqrt{3sin(t)}

=-1.588840129 + ?[/tex]

I get 0 for the limit, but according to Maple and my graphing calculator, that does not give the correct value for this integral. The correct value is approximately -2.8. May I please have some guidance as to what may have went wrong?