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(Solved): 1. Find the area of the plane region bounded by the curve y=x3 and the tangent line to this cur ...

$1. Find the area of the plane region bounded by the curve \( y=x^{3} \) and the tangent line to this curve at the point \( (1$

1. Find the area of the plane region bounded by the curve

y = x^{3}

and the tangent line to this curve at the point

(1, 1)

.

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To find the area of the plane region bounded by the curve =   and the tangent line to this curve at the point   , we need to determine the points of intersection between the curve and the tangent line.

First, let's find the equation of the tangent line at the point   . The slope of the tangent line can be found by taking the derivative of the curve at

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