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
To evaluate the integral (2x^3-5x^2+4x-1)\,dx, we will integrate each term separately using the power rule for integration, which states x^n\,dx = x^n+1n+1 + C. Step 1: Integrate the first term, 2x^3. 2x^3\,dx = 2 · x^3+13+1 = 2 · (x^4)/(4) = (x^4)/(2) Step 2: Integrate the second term, -5x^2. -5x^2\,dx = -5 · x^2+12+1 = -5 · (x^3)/(3) = -(5x^3)/(3) Step 3: Integrate the third term, 4x. 4x\,dx = 4 · x^1+11+1 = 4 · (x^2)/(2) = 2x^2 Step 4: Integrate the fourth term, -1. -1\,dx = -x Step 5: Combine all the integrated terms and add the constant of integration, C. (2x^3-5x^2+4x-1)\,dx = (x^4)/(2) - (5x^3)/(3) + 2x^2 - x + C The evaluated integral is: (x^4)/(2) - (5x^3)/(3) + 2x^2 - x + C Drop the next question.