MATH 31A Midterm: Math 31A Exam 17
Document Summary
Try to answer the following questions without the use of book, notes or calculator; but you can use the equation sheet posted on the course website. Time yourself and try to nish the questions in less than three hours: show that z /4. 4 an area and show how the areas piece together. ) tan x dx +z 1. 0 arctan x dx = (hint: interpret each integral as. First we note that we can change the dummy variables inside the integral. But since x = tan y if and only if y = arctan x (for x and y in this range), then these two integrals both involve the same curve. In particular, these integrals correspond to the respective areas shown below. 0 tan y dy y=arctan x or x=tan y. Since the two areas piece together to form a rectangle with dimensions 1 and. 4 then the combined area is the area of the rectangle which is.
