Calculus Limit Question?

Question

Write a limit to find the area between the x axis and the graph y=x^3 from x=1 to x=4. Then find the area.

Answer 1

Use Riemann Sum to caliculate by limits.

Interal: x = 1 = a to x =4 = b

Number of subintervals = n.

For each subinterval, we have a rectangle.

∆x = (4-1)/n = 3/n.

f(x ) = x³.

By using Right Riemann Sum we get,

Apply limit n → ∞ inorder to get exact value for area.

 

Therefore area is 255/4 or 63.75 square units.