two questions...(adsbygoogle = window.adsbygoogle || []).push({});

1) by a change of variable show the following...

[tex] \int^{\infty} _{-\infty} \frac{dt}{(a^2 + t^2)^{3/2}} = \frac{2}{a^2}\int^{\pi/2} _0 cos \ t \ dt [/tex]

i'm thinking about changing this to polar cords and see where that take me anyone?

2) [tex] F(x) = \int^{cos \ x} _0 e^{xt^2} \ dt , \ G(x) = \int^{cos \ x} _0 t^2 e^{xt^2} \ dt, \ H(t) = G(x) - F'(x) [/tex] express H(x) in elementry functions.

[tex] F'(x) = \frac{\partial cos \ x}{\partial x} e^{xt^2} - 0 + \int \frac{\partial}{\partial x} e^{xt^2} \ dt \\

= -sin \ x \ e^{xt^2} + \int t^2e^{xt^2} \ dt [/tex]

[tex]

H(x) = \int^{cos \ x} _0 t^2 e^{xt^2} \ dt + sin \ x \ e^{xt^2} - \int t^2e^{xt^2} \ dt

= sin \ x \ e^{xt^2} [/tex]

Did i do the dirv correctly? and how do I show that [tex]H(\pi/4) = \frac{e^{\pi/8}}{\sqrt{2}}[/tex]

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# Homework Help: Polar cords and integral help

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