a) The first integral corresponds to the area under y = f(x) on the interval [0, 3], which is a right triangle with base 3 and height 5, hence the integral is
b) The integral is zero since the areas under the curve over [3, 4] and [4, 5] are equal but opposite in sign. In other words, on the interval [3, 5], f(x) is symmetric and odd about x = 4, so
c) The integral over [5, 9] is the negative of the area of a rectangle with length 9 - 5 = 4 and height 5, so
Then by linearity, we have
Tony’s club is selling oranges to raise money. For every box they sell, they get 1 1/8 dollars profit. They have sold 75 boxes already. How many more boxes must they sell to raise 180 dollars?
Answer: We are given:
The amount of money Tony's club get for every box they sell dollar
They amount of money Tony's club has raised by selling 75 boxes is:
dollars
The amount of money Tony's club is required to raise = 180 dollars
The remaining need to be raised is :
dollars
Therefore, the number of more boxes to be sold are:
Hence, 85 more boxes they must sell to raise 180 dollars