How do you find the area bounded by the x axis, y axis, #y=x^2+1# and #x=2#?
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To find the area bounded by the xaxis, yaxis, the curve (y = x^2 + 1), and the line (x = 2), you need to integrate the function (y = x^2 + 1) with respect to x from the lower xvalue to the upper xvalue.

Determine the points of intersection between the curve (y = x^2 + 1) and the line (x = 2). This occurs at (x = 2) and (y = (2)^2 + 1 = 5).

Set up the integral for the area: [A = \int_{0}^{2} (x^2 + 1) , dx] The lower limit is (x = 0) (the yaxis) and the upper limit is (x = 2) (the line (x = 2)).

Integrate the function (x^2 + 1) with respect to (x) from 0 to 2.

Evaluate the integral: [A = \left[\frac{x^3}{3} + x\right]_{0}^{2}] [A = \left[\frac{(2)^3}{3} + 2\right]  \left[\frac{(0)^3}{3} + 0\right]] [A = \left[\frac{8}{3} + 2\right]  0] [A = \frac{8}{3} + 2] [A = \frac{8}{3} + \frac{6}{3}] [A = \frac{14}{3}]
Therefore, the area bounded by the xaxis, yaxis, the curve (y = x^2 + 1), and the line (x = 2) is (\frac{14}{3}) square units.
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When evaluating a onesided 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 onesided 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 onesided 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 onesided 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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