Changing the order of integration practice problems
Integrals you cannot do in the given order: sketch the region and swap dx and dy. 7 problems with worked solutions; in 7 of them every equation is proved by a computer algebra system.
Evaluate \( \displaystyle \int\limits_{0}^{1}\int\limits_{y}^{1} \sin{\left(x^{2} \right)}\, dx\, dy \) by reversing the order of integration.
Evaluate \( \displaystyle \int\limits_{0}^{1}\int\limits_{\sqrt{x}}^{1} \sqrt{y^{3} + 1}\, dy\, dx \) by reversing the order of integration.
Evaluate \( \displaystyle \int\limits_{0}^{2}\int\limits_{x}^{2} e^{y^{2}}\, dy\, dx \) by reversing the order of integration.
Evaluate \( \displaystyle \int\limits_{0}^{1}\int\limits_{\sqrt{y}}^{1} e^{x^{3}}\, dx\, dy \) by reversing the order of integration.
Evaluate \( \displaystyle \int\limits_{0}^{1}\int\limits_{x^{2}}^{1} x \cos{\left(y^{2} \right)}\, dy\, dx \) by reversing the order of integration.
Evaluate \( \displaystyle \int\limits_{0}^{1}\int\limits_{x}^{1} e^{y^{2}}\, dy\, dx \) by reversing the order of integration.
Evaluate \( \displaystyle \int\limits_{0}^{2}\int\limits_{y}^{2} \sin{\left(x^{2} \right)}\, dx\, dy \) by reversing the order of integration.