Integrals of absolute values practice problems
Split the interval where the integrand changes sign, then integrate each piece. 10 problems with worked solutions; in 10 of them every equation is proved by a computer algebra system.
Evaluate \( \displaystyle \int_{-1}^{3} \left| 4 - 2 x \right| dx \).
Evaluate \( \displaystyle \int_{-3}^{-1} \left| - 2 x - 4 \right| dx \).
Evaluate \( \displaystyle \int_{-3}^{2} \left| - x^{2} - x \right| dx \).
Evaluate \( \displaystyle \int_{-2}^{5} \left| x^{2} - 2 x - 3 \right| dx \).
Evaluate \( \displaystyle \int_{-1}^{3} \left| - x^{2} + 3 x - 2 \right| dx \).
Evaluate \( \displaystyle \int_{-1}^{6} \left| x^{2} - 4 x + 3 \right| dx \).
Evaluate \( \displaystyle \int_{-2}^{1} \left| - x \right| dx \).
Evaluate \( \displaystyle \int_{-5}^{1} \left| - 3 x - 6 \right| dx \).
Evaluate \( \displaystyle \int_{2}^{4} \left| x - 3 \right| dx \).
Evaluate \( \displaystyle \int_{-5}^{-1} \left| - x - 2 \right| dx \).