Exercise
$\int_{x^{2}}^{x^{3}}\left(t^{3}-2t\right)dt$
Step-by-step Solution
Learn how to solve problems step by step online. Integrate the function t^3-2t from x^2 to x^3. Expand the integral \int_{x^2}^{x^3}\left(t^3-2t\right)dt into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int_{x^2}^{x^3} t^3dt results in: \frac{x^{12}}{4}+\frac{-x^{8}}{4}. Gather the results of all integrals. Combine fractions with common denominator 4.
Integrate the function t^3-2t from x^2 to x^3
Final answer to the exercise
$\frac{-x^{8}+x^{12}}{4}+x^{4}-x^{6}$