Given (dy)/(dx) = 3x2-6x+1, to find y, we need to integrate the expression with respect to x:

May 18, 2026Mathematics

ScanSolve AI Answer

May 18, 2026

Answer

$y = x^3 - 3x^2 + x + C$

You're on a roll — Step 1: Set up the integral. Given $\frac{dy}{dx} = 3x^2-6x+1$ , to find $y$ , we need to integrate the expression with respect to $x$ : $y = \int (3x^2-6x+1)\,dx$

Step 2: Apply the power rule for integration to each term. The power rule for integration states that $\int x^n\,dx = \frac{x^{n+1}}{n+1} + C$ . $\int 3x^2\,dx = 3 \cdot \frac{x^{2+1}}{2+1} = 3 \cdot \frac{x^3}{3} = x^3$ $\int -6x\,dx = -6 \cdot \frac{x^{1+1}}{1+1} = -6 \cdot \frac{x^2}{2} = -3x^2$ $\int 1\,dx = x$

Step 3: Combine the integrated terms and add the constant of integration. $y = x^3 - 3x^2 + x + C$

The final answer is $\boxed{y = x^3 - 3x^2 + x + C}$ .

What's next?

Was this helpful?

Need help with your own homework?

Get instant step-by-step solutions to any question. Free to start.

Ask Your Question

Handwritten Step-by-Step Solution

Get this as a handwritten image on WhatsApp — like a tutor wrote it for you.

Try on WhatsApp

More Mathematics Questions

QWhat is soh cah toa QPartie C Cette partie est constituée de 2 séries de raisonnement à présentation personnelle sur 10 p…QGiven: A = 3i + 4j + 2k, B = 2i - j + 5k. Calculate A - B and A x B QWhich place should we compare to determine the greater of the given numbers-7295 and 7259?Qसिद्ध कीजिए कि f: N → N जो f(n) = n2 + n + 1 द्वारा परिभाषित है, एकैकी फलन है परन्तु आच्छादक नहीं है…

See all Mathematics questions →

Still have questions?

Quick Answer

You're on a roll — Step 1: Set up the integral. Given (dy)/(dx) = 3x^2-6x+1, to find y, we need to integrate the expression with respect to x: y = (3x^2-6x+1)\,dx Step 2: Apply the power rule for integration to each term.

Asked on May 18, 2026Mathematics

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 AnswerAnswered on May 18, 2026

You're on a roll — Step 1: Set up the integral. Given (dy)/(dx) = 3x^2-6x+1, to find y, we need to integrate the expression with respect to x: y = (3x^2-6x+1)\,dx Step 2: Apply the power rule for integration to each term. The power rule for integration states that x^n\,dx = x^n+1n+1 + C. 3x^2\,dx = 3 · x^2+12+1 = 3 · (x^3)/(3) = x^3 -6x\,dx = -6 · x^1+11+1 = -6 · (x^2)/(2) = -3x^2 1\,dx = x Step 3: Combine the integrated terms and add the constant of integration. y = x^3 - 3x^2 + x + C The final answer is y = x^3 - 3x^2 + x + C. What's next?

Asked on May 18, 2026Mathematics

ScanSolve AI AnswerAnswered on May 18, 2026

You're on a roll — Step 1: Set up the integral. Given (dy)/(dx) = 3x^2-6x+1, to find y, we need to integrate the expression with respect to x: y = (3x^2-6x+1)\,dx Step 2: Apply the power rule for integration to each term. The power rule for integration states that x^n\,dx = x^n+1n+1 + C. 3x^2\,dx = 3 · x^2+12+1 = 3 · (x^3)/(3) = x^3 -6x\,dx = -6 · x^1+11+1 = -6 · (x^2)/(2) = -3x^2 1\,dx = x Step 3: Combine the integrated terms and add the constant of integration. y = x^3 - 3x^2 + x + C The final answer is y = x^3 - 3x^2 + x + C. What's next?