Question

Evaluate the integral ∫82x⁸(9x²)(x - 1) dx. (Remember to use absolute values where appropriate. Use c for the constant of integration.)

Answer 1

To evaluate the integral of 82x⁸(9x²)(x - 1) dx, simplify and integrate term by term, resulting in the final answer 67.09x¹² - 67.09x¹¹ + c, with 'c' representing the integration constant.

Step-by-step explanation:

The integral in question is ∨82x⁸(9x²)(x - 1) dx. To evaluate it, we must simplify and integrate term by term. The first step is to multiply out the integrand:

82x⁸ × 9x² × (x - 1) = 738x¹¹ - 738x¹°

Now, we integrate each term separately:

1. ∨738x¹¹ dx = 738 × ¹±ⁱ² x¹² ¹² + c = 67.09x¹² + c
2. ∨738x¹° dx = 738 × ¹ⁱ¹ x¹¹ + c = 67.09x¹¹ + c

Adding these together gives us the final answer:

67.09x¹² - 67.09x¹¹ + c, where 'c' is the constant of integration.