find area under curve

Question

Using the left-had approximation method with 5 equal subintervals, find the area under the curve f(x)=√(1+x³) on the interval [0,1].

 

a.) 1.074

b.) 1.156

c.) 2.356

d.) 1.110

Answer 1

Jas, I hope I can still help!

 

Alright, first we have to find the width of each triangle.  The formula for that is Δx = (b-a)/n. Since n = 5, we have (1-0)/5 = .2

 

Since we are using left-hand approximation, our x-coordinates are 0, .2, .4, .6, and .8

 

In order to find the area of a rectangle, we multiply the length x width. We have width, but we need height.  To do this, we plug in the x coordinate to the given formula to get y (the height).  Since we would multiply each height by .2, we can add the heights together, then multiply by the width one time.

 

Soooo, we have [√(1+0³) + √(1+.2³) + √(1+.4³) + √(1+.6³) + √(1+.8³)](.2) = 1.074

 

Boom.