Syllabus for MATH 19B Pedro Morales

tment of Mathematics - Google Chrome 1431/TB/ch6/s62/index.html In Exercises 11-18, evaluate the integrals by finding an antiderivative and using the Fundamental Theorem of Calculus. 11. 2x dx 12. 3x2 d 13. e dx π12 14. sin x d 15. cosx dx Math 1431 Page I of 3 Section 6.2 Exercise

Consider the integral I =e-x2 dx. Can you think of an integration technique that could help you evaluate I? Evaluate I using Integrate. Explain why you think the following identity is correct: Rewrite the above integral using polar coordinates and evaluate Consider the integral x dz dy dx. Evaluate this integral in Mathematica. Sketch the region of integration using RegionPlot3D. Use the sketch of the region plotted in the previous part to set up an equivalent integral but in a different order of integration. Evaluate in Mathematica and comment. Consider the integral x dz dy dx. Evaluate this integral in Mathematica. Sketch the region of integration using RegionPlot3D. Use the sketch of the region plotted in the previous part to set up an equivalent integral but in a different order of integration. Evaluate in Mathematica and comment.