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1. \int_{0}^{1} - x^{2} + x\, dx

   First find an antiderivative F, then evaluate F(b) − F(a).

2. \int - x^{2} + x\, dx = \int - x^{2}\, dx + \int x\, dx

   The integral of a sum is the sum of the integrals.

3. \int - x^{2}\, dx = -1 \int x^{2}\, dx

   Pull the constant -1 out of the integral.

4. \int x^{2}\, dx = \frac{x^{3}}{3}

   Power rule: ∫xⁿ dx = xⁿ⁺¹/(n+1) (n ≠ −1).

5. \int x\, dx = \frac{x^{2}}{2}

   Power rule: ∫xⁿ dx = xⁿ⁺¹/(n+1) (n ≠ −1).

6. F(1) - F(0) = \left(\frac{1}{6}\right) - \left(0\right)

   Fundamental theorem of calculus: plug in the limits.

7. = \frac{1}{6}

   Simplify.

Otkrij odgovor

\frac{1}{6}