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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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UkoKoshka [18]

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Step-by-step explanation:

Simplify  \frac{1}{8}(x-4)

8

1

​

(x−4)  to  \frac{x-4}{8}

8

x−4

​

.

-\frac{x-4}{8}=-4

−

8

x−4

​

=−4

2 Multiply both sides by 88.

-x+4=-4\times 8

−x+4=−4×8

3 Simplify  4\times 84×8  to  3232.

-x+4=-32

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4 Regroup terms.

4-x=-32

4−x=−32

5 Subtract 44 from both sides.

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6 Simplify  -32-4−32−4  to  -36−36.

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7 Multiply both sides by -1−1.

x=36

x=36

6 0
3 years ago
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