Evaluate the integral: integral (2x3-5x2+4x−1) dx

Question

ScanSolve AI Tutor · Accepted Answer

To evaluate the integral ∫ (2x³−5x²+4x−1) dx, we will integrate each term separately using the power rule for integration, which states ∫ xⁿ dx = (xⁿ⁺¹)/(n+1) + C. Step 1: Integrate the first term, 2x³. ∫ 2x³ dx = 2 · (x³⁺¹)/(3+1) = 2 · (x⁴)/(4) = (x⁴)/(2) Step 2: Integrate the second term, −5x². ∫ −5x² dx = −5 · (x²⁺¹)/(2+1) = −5 · (x³)/(3) = −(5x³)/(3) Step 3: Integrate the third term, 4x. ∫ 4x dx = 4 · (x¹⁺¹)/(1+1) = 4 · (x²)/(2) = 2x² Step 4: Integrate the fourth term, −1. ∫ −1 dx = −x Step 5: Combine all the integrated terms and add the constant of integration, C. ∫ (2x³−5x²+4x−1) dx = (x⁴)/(2) − (5x³)/(3) + 2x² − x + C The evaluated integral is: (x⁴)/(2) − (5x³)/(3) + 2x² − x + C

Evaluate the integral: integral (2x3-5x2+4x-1)\,dx

Answer

Step-by-step solution

Integrate the first term, $2x^3$ .

Integrate the second term, $-5x^2$ .

Integrate the third term, $4x$.

Integrate the fourth term, $-1$ .

Combine all the integrated terms and add the constant of integration, $C$ .

Try one yourself

Still stuck on this one?

More Mathematics Questions