You need to split the area under the graph in n rectangles that have the widths `Delta x` and the heights`f(x_i).`

You need to evaluate the area of each rectangle such that:

`A = f(x_i)*Delta x`

Adding all these areas of the rectangles yields:

Area = `sum_(i=1)^n` `f(x_i)*Delta...

## See

This Answer NowStart your **48-hour free trial** to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.

Already a member? Log in here.

You need to split the area under the graph in n rectangles that have the widths `Delta x` and the heights`f(x_i).`

You need to evaluate the area of each rectangle such that:

`A = f(x_i)*Delta x`

Adding all these areas of the rectangles yields:

Area = `sum_(i=1)^n``f(x_i)*Delta x`

You need to evaluate Delta x over interval `[0,pi/2]` such that:

`Delta x = (pi/2 - 0)/n = pi/(2n)`

Using the right endpoints, you may evaluate `f(x_i)` such that:

`x_i= 0 + i*Delta x = i*pi/(2n)`

`f(x_i) = 9*x_i*cos(9x_i)`

`f(x_i)*Delta x = 9i*pi/(2n)*pi/(2n)*cos(9i*pi/(2n))`

**Hence, evaluating the area using limit definition yields:**

**Area = `lim_(n-gtoo)` `sum_(i=1)^n` `9i(pi^2)/(4n^2)cos(9i*pi/(2n))` **