To calculate: The integral
Answer to Problem 19E
Thevalue of the integral
Explanation of Solution
Given:
The integral is
Concept used:
If a nonnegative function
Formula used:
The area of the trapezium is as follows:
Calculation:
In the given integral, the integrand function
Draw the graph of the function
Substitute 0 for
Substitute 1 for
Substitute -1 for
Substitute 2 for
Substitute
Substitute 3 for
Substitute
It can be seen that there are two lines intersects at point
Now draw the graph of
It can be seen that the area under a curve from
The base or height of the left trapezoid can be calculated as,
It can be seen from Figure 1 that the parallel sides of the left trapezoid are
Use the formula of the trapezium to obtain the area of the left trapezoid
The base or height of the right trapezoid can be calculated as,
It can be seen from Figure 1 that the parallel sides of the right trapezoid are
Use the formula of the trapezium to obtain the area of the right trapezoid
Find the sum of
Therefore, by the concept the value of the integral is equal to the sum of the area of two trapezoids.
The value of the integral
Conclusion:
Thus, thevalue of the integral
Chapter 6 Solutions
Calculus: Graphical, Numerical, Algebraic
Additional Math Textbook Solutions
Calculus & Its Applications (14th Edition)
Single Variable Calculus: Early Transcendentals (2nd Edition) - Standalone book
Calculus, Single Variable: Early Transcendentals (3rd Edition)
Precalculus (10th Edition)
Thomas' Calculus: Early Transcendentals (14th Edition)
Calculus and Its Applications (11th Edition)
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