To calculate: The
Answer to Problem 14E
The value 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 is
Draw the graph of the function
Substitute 0 for
Substitute 1 for
Substitute 2 for
The coordinates are
Now draw the graph of
It can be seen that the area under a line from
The base or height of the trapezoid can be calculated as,
It can be seen from Figure 1 that the parallel sides of the trapezoid are
Use the formula of the trapezium to obtain the area of the trapezoid.
Therefore, by the concept the value of the integral is equal to the area of the trapezoid.
The value of the integral
Conclusion:
Thus, the value of the integral
Chapter 6 Solutions
Calculus: Graphical, Numerical, Algebraic: Solutions Manual
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