Determine a region whose area is equal to the given limit. Do not evaluate the limit.

Question

A). √(1+x) on [-3,3]

B). 3√(1-x) on [0,3]

C). √(1+x) on [0,3]

D). 3√(1+x) on [-3,3]

E). 3√(1+x) on [0,3]

Please show the whole process step by step.

Answer 1

Let 3/n be the delta x and (3/n)i be the x for the RHS of a rectangle under the curve sqrt(1+x)

The limit as n goes to infinity will take an infinite sum of rectangles of width dx and height sqrt(1+x) (C)

Answer 2

desmos.com/calculator/dgdpflg3dg

Use the slider on n to see the Riemann sum approach the value of the definite integral.