How do you find the area #y = f(x) = 4/x^2# , from 1 to 2 using ten approximating rectangles of equal widths and right endpoints?

1 Answer
Sep 24, 2015

Answer:

See the explanation.

Explanation:

#y = f(x) = 4/x^2# , on #[1,2]# using #n=10# approximating rectangles of equal widths and right endpoints.

#Deltax = (b-a)/n = (2-1)/10=0.1#

The bases of the rectangles are the subintervals:

#[1,1.1], [1.1,1.2], [1.2,1.3], . . . , [1.8,1.9], [1.9,2]#

The right endpoints are :

#1.1, 1.2, 1.3, . . . , 1.9, 2#

Use these to find the height of the rectangles:

#f(1.1)=4/1.1^2, f(1.2)=4/1.2^2, . . . , f(1.9) = 4/1.9^2, f(2)=4/2^2#

So the areas of the rectangles are #f(x_i)Deltax# for these various #x_i# and the Riemann sum is:

#4/1.1^2Delta x+4/1.2^2 Delta x+ * * * +4/1.9^2Delta x+4/2^2Delta x#

# = (4/1.1^2+4/1.2^2 + * * * +4/1.9^2+4/2^2)Delta x#

# = (4/1.1^2+4/1.2^2 + * * * +4/1.9^2+4/2^2)(0.1)#

Now do the arithmetic.