I will assume you want me to demonstrate the integration process for Exercise 6 (1)a. This means I will find the function whose indefinite integral is given by the expression in (1)a, and then integrate that function to verify the result. Given answer for Exercise 6 (1)a: $F(x) = 4x^3 + 3x^2 - 5x + c$. Step 1: Determine the function $f(x)$ that was integrated to obtain $F(x)$. To do this, we find the derivative of $F(x)$. $$f(x) = \frac{d}{dx}(4x^3 + 3x^2 - 5x + c)$$ $$f(x) = 4 \cdot 3x^{3-1} + 3 \cdot 2x^{2-1} - 5 \cdot 1x^{1-1} + 0$$ $$f(x) = 12x^2 + 6x - 5$$ Step 2: Integrate $f(x)$ to verify the given answer. We need to find $\int (12x^2 + 6x - 5)\,dx$. Using the power rule for integration, $\int x^n\,dx = \frac{x^{n+1}}{n+1} + C$: $$\int (12x^2 + 6x - 5)\,dx = \int 12x^2\,dx + \int 6x\,dx - \int 5\,dx$$ $$= 12 \left(\frac{x^{2+1}}{2+1}\right) + 6 \left(\frac{x^{1+1}}{1+1}\right) - 5x + c$$ $$= 12 \left(\frac{x^3}{3}\right) + 6 \left(\frac{x^2}{2}\right) - 5x + c$$ $$= 4x^3 + 3x^2 - 5x + c$$ The result matches the given expression. The verified indefinite integral is: $$\boxed{\mathbf{4x^3 + 3x^2 - 5x + c}}$$ Send me the next one 📸