# How do you find the area under the curve #f(x)=x^2# on the interval [-1,1]?

Area under a curve on an interval is analogous to the integral of the function of the curve on an interval.

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To find the area under the curve (f(x) = x^2) on the interval ([-1, 1]), you can integrate the function over that interval using the definite integral formula. So, integrate (x^2) from -1 to 1 with respect to (x). The integral of (x^2) with respect to (x) is (\frac{x^3}{3}). Evaluate this expression from -1 to 1, then subtract the value of the integral at the lower limit from the value at the upper limit to find the area under the curve.

[ \int_{-1}^{1} x^2 dx = \left[\frac{x^3}{3}\right]_{-1}^{1} = \left(\frac{1^3}{3}\right) - \left(\frac{(-1)^3}{3}\right) = \frac{1}{3} - \left(-\frac{1}{3}\right) = \frac{2}{3} ]

So, the area under the curve (f(x) = x^2) on the interval ([-1, 1]) is (\frac{2}{3}).

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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.

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.

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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