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In Exercises 49–58, sketch the region determined by the iterated integral and then evaluate the integral. For some of these integrals, it may be helpful to reverse the order of integration.

0π40secxsecxdydx

Short Answer

Expert verified

Value of the given integral is:1

Step by step solution

01

Step 1. Given Information 

An integral,0π40secxsecxdydx

02

Step 2. Sketching the region of integration 

Region of integration is shaded in the graph below.

03

Step 3. Evaluating the given iterated integral  

Given integral,

0π40secxsecxdydx=0π4secx(y)0secxdx=0π4secxsecx-0dx=0π4sec2xdx=tanx0π4=tanπ4-tan0=1-0=1

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