To calculate: The
Answer to Problem 18E
Thevalue of the integral
Explanation of Solution
Given:
The integral is
Concept used:
If a nonnegative function
Formula used:
The area of the semicircle is as follows:
Here, the expression
Calculation:
In the given integral, the integrand function is
For values of x greater than or equal to 0 the value of function will be
For values of x less than 0 the value of function will be
Put the value of x = 0, 1, 2 for coordinates of y , we get
For x = 0,
For x = 1,
For x = 2,
Thus the coordinates are (0, 1), (1, 0), (2, -1).
Put the value of x = 0, -1, -2 for coordinates of y , we get
For x = 0,
For x = -1,
For x = -2,
Thus the coordinates are (0, 1), (-1, 0), (-2, -1).
Now draw the graph of
It can be seen from Figure 1 that the area under a function is two triangles. The height of the left triangle is 1 unit and the base is 1 unit.
The height of the right triangle is on the left side is 1 unit and the length of the base is 1 unit.
The area of the region bounded by the
Use the formula of the triangle to obtain the area of the triangle.
Therefore, by the concept the value of the integral is equal to the area of the sum of two triangles.
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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