This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Welcome back online — missed you this week. To evaluate the integral (2x)(2x)\,dx, we can use a substitution method. Step 1: Set up the substitution. Let u = (2x). Step 2: Find the differential du. Differentiate u with respect to x: (du)/(dx) = (d)/(dx)((2x)) = (2x) · 2 So, du = 2(2x)\,dx. Step 3: Express (2x)\,dx in terms of du. From the previous step, we have du = 2(2x)\,dx. Dividing by 2 gives: (2x)\,dx = (1)/(2)du Step 4: Substitute u and du into the integral. The integral becomes: u · (1)/(2)du Step 5: Integrate with respect to u. (1)/(2) u\,du = (1)/(2) · (u^2)/(2) + C = (u^2)/(4) + C Step 6: Substitute back u = (2x). (((2x))^2)/(4) + C = (^2(2x))/(4) + C The final answer is (^2(2x))/(4) + C. Send me the next one 📸