Final Answer
$-\frac{4}{3}$
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Step-by-step Solution
Problem to solve:
$\int_{-1}^{1}\left(x^2-1\right)dx$
Specify the solving method
1
Expand the integral $\int_{-1}^{1}\left(x^2-1\right)dx$ into $2$ integrals using the sum rule for integrals, to then solve each integral separately
$\int_{-1}^{1} x^2dx+\int_{-1}^{1}-1dx$
Learn how to solve definite integrals problems step by step online.
$\int_{-1}^{1} x^2dx+\int_{-1}^{1}-1dx$
Learn how to solve definite integrals problems step by step online. Integrate the function x^2-1 from -1 to 1. Expand the integral \int_{-1}^{1}\left(x^2-1\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int_{-1}^{1} x^2dx results in: \frac{2}{3}. The integral \int_{-1}^{1}-1dx results in: -2. Gather the results of all integrals.
Final Answer
$-\frac{4}{3}$