Home > Calculus > Integration: the Area Problem

What is the area under the curve #y=sqrtt# from 0 to 1?

Answer 1

Aurora Alvarado

The area is given by the integral #int_0^1sqrttdt=int_0^1(t^(3/2)/(3/2))'dt=2/3#

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Answer 2

Aurora Alvarado

To find the area under the curve y = √t from t = 0 to t = 1, integrate √t with respect to t from 0 to 1. The integral of √t with respect to t from 0 to 1 is equal to 2/3. Therefore, the area under the curve y = √t from t = 0 to t = 1 is 2/3 square units.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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