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Chapter 13: Q. 55 (page 1016)

In Exercises 49鈥�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.

鈭�01鈭�y1ex2dxdy

Short Answer

Expert verified

Value of the given integral is:e-12

Step by step solution

01

Step 1. Given Information

An integral,鈭�01鈭�y1ex2dxdy

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,

鈭�01鈭�y1ex2dxdy

Changing the order of integration,

鈭�01鈭�0xex2dydx=鈭�01ex2y0xdx=鈭�01ex2x-0dx=鈭�01xex2dx

Put, putx2=t,2xdx=dt,

We get, 鈭�01et2dt

=et201=e1-e02=e-12

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