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∫x2dx\int x^{2}dx

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Full solution

Q. ∫x2dx\int x^{2}dx
  1. Identify integral: Identify the integral that needs to be solved.\newlineWe need to find the indefinite integral of x2x^2 with respect to xx, which is written as ∫x2 dx\int x^2 \, dx.
  2. Apply power rule: Apply the power rule for integration.\newlineThe power rule for integration states that ∫xn dx=x(n+1)n+1+C\int x^n \, dx = \frac{x^{(n+1)}}{n+1} + C, where CC is the constant of integration.
  3. Calculate integral: Calculate the integral using the power rule.\newlineUsing the power rule, we have ∫x2 dx=x2+12+1+C=x33+C\int x^2 \, dx = \frac{x^{2+1}}{2+1} + C = \frac{x^3}{3} + C.
  4. Write final answer: Write the final answer.\newlineThe integral of x2x^2 with respect to xx is (x3)/3+C(x^3)/3 + C.

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