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Hi,

So this might be overwhelmingly stupid... But the fundamental theorem of calculus states:

[tex]\int_{a}^{b}f(x)dx=F(b)-F(a)[/tex]

Where F is any antiderivative of f.

So I have this very simple integral that I'm trying to solve...:

[tex]2\pi\int_{0}^{2}x^3\sqrt{1+9x^4}dx\rightarrow \ u=1+9x^4[/tex]

[tex]=\frac{\pi}{18}*\frac{2}{3}u^{3/2}\mid_{1}^{145}=\frac{\pi}{27}(1+9x^4)^{3/2}\mid_{1}^{145}[/tex]

For the answer, I'm given the following:

[tex]\frac{\pi}{27}(145\sqrt{145}-1)[/tex]

However, when I use the fundamental theorem of calculus, I get something nasty:

[tex]\frac{\pi}{27}[(1+9(145)^4)^{3/2}-(1+9(1)^4)^{3/2}][/tex]

[tex]\mbox{calculator gives}=\frac{2}{27}[(1989227813\sqrt{1989227813}-5\sqrt{5})*\pi*\sqrt{2}]}[/tex]

I don't know why I keep getting the wrong thing. I'm obviously making some sort of stupid error. Any suggestions?

So this might be overwhelmingly stupid... But the fundamental theorem of calculus states:

[tex]\int_{a}^{b}f(x)dx=F(b)-F(a)[/tex]

Where F is any antiderivative of f.

So I have this very simple integral that I'm trying to solve...:

[tex]2\pi\int_{0}^{2}x^3\sqrt{1+9x^4}dx\rightarrow \ u=1+9x^4[/tex]

[tex]=\frac{\pi}{18}*\frac{2}{3}u^{3/2}\mid_{1}^{145}=\frac{\pi}{27}(1+9x^4)^{3/2}\mid_{1}^{145}[/tex]

For the answer, I'm given the following:

[tex]\frac{\pi}{27}(145\sqrt{145}-1)[/tex]

However, when I use the fundamental theorem of calculus, I get something nasty:

[tex]\frac{\pi}{27}[(1+9(145)^4)^{3/2}-(1+9(1)^4)^{3/2}][/tex]

[tex]\mbox{calculator gives}=\frac{2}{27}[(1989227813\sqrt{1989227813}-5\sqrt{5})*\pi*\sqrt{2}]}[/tex]

I don't know why I keep getting the wrong thing. I'm obviously making some sort of stupid error. Any suggestions?

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