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Wittaler [7]
3 years ago
14

Evaluate exactly the value of the integral from -1 to 0 (2x^4+8x)^3 (4x^3+4),dx. Include the use of substitution and the antider

ivative.
Mathematics
1 answer:
ddd [48]3 years ago
3 0
Hello,

Let's be

 z=2x^4+8x \\
dz=(8x^3+8)\ dx=8(x^3+1)\ dx \\

 \int\limits^0_{-1} {(2x^4+8x)^3*(4x^3+4)} \, dx =4* \int\limits^0_{-6} { \dfrac{z^3}{2}} \, dz \\
= 2* \left[\begin{array}{ccc} \dfrac{z^4}{4}\end{array}\right] ^0_{-6}=
\left[\begin{array}{ccc} \dfrac{z^4}{2}\end{array}\right] ^0_{-6}=0-648=-648

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Now, to check that we're right, we need to subtract 2 3's from 7.

We do this by multiplying 2X3 (to get 6) and then writing:

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 ----

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 -6 |     <---that's supposed to be an arrow reminding you that we're

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