Question

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 antiderivative.

Answer 1

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) { (z^3)/(2)} \, dz \\ = 2* \left[\begin{array}{ccc} (z^4)/(4)\end{array}\right] ^0_(-6)= \left[\begin{array}{ccc} (z^4)/(2)\end{array}\right] ^0_(-6)=0-648=-648`