Find the area between the curve y=4/x and the x-axis from x=1 to x=e.
It is a review question for my final exam and I am really stuck on how to solve
You should hope for a final exam question so easy.
area= INT y dx= INT 4/x dx from 1 to e
area= 4ln x from 1 to e
To find the area between the curve y = 4/x and the x-axis from x = 1 to x = e, you can use integration.
First, set up the integral:
area = ∫[1 to e] 4/x dx
To integrate, you can rewrite the integral as:
area = 4 ∫[1 to e] 1/x dx
Now, integrate 1/x with respect to x:
area = 4 ln|x| [1 to e]
Substitute the limits of integration:
area = 4 ln(e) - 4 ln(1)
Since ln(1) is equal to 0, the equation simplifies to:
area = 4 ln(e)
Since ln(e) is equal to 1, the final result is:
area = 4
So, the area between the curve y = 4/x and the x-axis from x = 1 to x = e is 4.