Question

Question #bde9c

Answer 1

See below.

Explanation:

An approximation to the area formula

`A=int_(x_i)^(x_f)f(x)dx` can be done using the sum

`A_n=sum_(k=0)^(k=n)f(x_i+k Delta x)Delta x`

where `Delta x = (x_f-x_i)/n`. Applying this to

`f(x)=4sin(x)` we will have better approximations as `n` increases

Attached the realization of `A_2, A_5` and `A_(10)`

The computed values are shown in the following table

`((2,5,10,50,100),(6.28319,7.73506,7.93409,7.99737,7.99934))`