You need to write a program to calculate the area under a curve

: f(x) = 5x3 + 7x2 3x + 4

for a <= x <= b where a and b are greater than or equal to 0.

First, use cin to input the values of a and b which are defined as double. Check whether a and b are larger than 0, and whether a is smaller than or equal to b. If NOT, display an error message and exit. If YES, your program approximates the area under the curve between a and b by partitioning the area into small segments where each segment has width w.

For each area calculation, your program should calculate areas for w, w/2, w/4, , starting with w=(b-a)/10. Your program should keep calculating more accurate areas until the difference between the last two of your calculations is less than .0001. Then the program should display the last area value calculated.

See pseudo code below.

Example Output:

Example 1: Enter value a: 2 Enter value b: 7 Result is 3715.42

Example 2: Enter value a: 5.3 Enter value b: 8.2 Result is 5557.23

Example 3: Enter value a: 2.6 Enter value b: -7.9 Invalid data, either a or b is < 0

Example 4: Enter value a: 6 Enter value b: 3.9 Invalid data, a > b