Explanation Given Information: The provided function is ∫ ln ( π / 2 ) ln ( π ) e x sin ( e x ) d x . Formula Used: If u is a function of x, then the rule to evaluate an integral is ∫ f d x = ∫ ( f d u / d x ) d u where d u d x a derivative of the function with respect to x and solve for d x in terms of d u . If f be a function that is continuous and defined over the interval [ a , b ] , then the integral of the function defined on that interval is given by: ∫ a b f ( u ) d u = F ( b ) − F ( a ) If the function is f ( x ) = sin ( a x ) , then the formula for the integration of the function is given by ∫ sin ( a x ) d x = − 1 a cos ( a x ) + C . Calculation: Consider the function ∫ ln ( π / 2 ) ln ( π ) e x sin ( e x ) d x . Replace the parenthetical expression with variable u . u = e x Determine the derivative of u with respect to x , d u d x = d d x e x d u d x = e x Determine the value of d x , d x = 1 e x d u Replace the value of upper limit b by substituting x = ln ( π ) in e x , b = e x b = e ln ( π ) b = π Replace the value of lower limit a by substituting x = ln ( π 2 ) in e x a = e x a = e ln ( π 2 ) a = π 2 Substitute the value of d x into the integral

Finite Mathematics and Applied Calculus (MindTap Course List)

7th Edition

ISBN: 9781337274203

Author: Stefan Waner, Steven Costenoble

Publisher: Cengage Learning

See similar textbooks

Videos

Question

Chapter 16, Problem 21RE

To determine

To calculate: The integral of the function ∫ln(π/2)ln(π)exsin(ex) dx.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 16, Problem 20RE

Chapter 16, Problem 22RE

Students have asked these similar questions

find the zeros of the function algebraically: f(x) = 9x2 - 3x - 2

Rylee's car is stuck in the mud. Roman and Shanice come along in a truck to help pull her out. They attach one end of a tow strap to the front of the car and the other end to the truck's trailer hitch, and the truck starts to pull. Meanwhile, Roman and Shanice get behind the car and push. The truck generates a horizontal force of 377 lb on the car. Roman and Shanice are pushing at a slight upward angle and generate a force of 119 lb on the car. These forces can be represented by vectors, as shown in the figure below. The angle between these vectors is 20.2°. Find the resultant force (the vector sum), then give its magnitude and its direction angle from the positive x-axis. 119 lb 20.2° 377 lb

An airplane flies due west at an airspeed of 428 mph. The wind blows in the direction of 41° south of west at 50 mph. What is the ground speed of the airplane? What is the bearing of the airplane?

Chapter 16 Solutions

Finite Mathematics and Applied Calculus (MindTap Course List)

Ch. 16.1 - Prob. 1E Ch. 16.1 - Prob. 2E Ch. 16.1 - Prob. 3E Ch. 16.1 - Prob. 4E Ch. 16.1 - Prob. 5E Ch. 16.1 - Prob. 6E Ch. 16.1 - Prob. 7E Ch. 16.1 - Prob. 8E Ch. 16.1 - Prob. 9E Ch. 16.1 - Prob. 10E

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

The integral of the function ∫ ln ( π / 2 ) ln ( π ) e x sin ( e x ) d x .

Solution Summary: The author explains how to calculate the integral of the function displaystyle

Videos

To calculate: The integral of the function ∫ln(π/2)ln(π)exsin(ex) dx.

Want to see the full answer?

Chapter 16 Solutions