   Chapter 15.1, Problem 20E

Chapter
Section
Textbook Problem

Calculate the iterated integral.20. ∫ 1 3 ∫ 1 5 ln y x y d y   d x

To determine

To estimate: The value of given iterated integral.

Explanation

Formula used:

If g(x) is the function of x and h(y) is the function of y, then,

abcdg(x)h(y)dydx=abg(x)dxcdh(y)dy

Calculation:

Compute the given iterated integral by using the formula stated above.

1315(lnyxy)dydx=131xdx15lnyydy=[lnx]1315lnyydy

In order to integrate 15lnyydy , substitute t=lny .

Then, dt=1ydy .

Therefore, the required integral value is obtained as follows

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