Prob. 11 Find the area of the region between the following graphs if possible. 1. $f(x) = x^2 + 2x + 1$, and $g(x) = 3x + 3$ 2. Find the area of the region bounded by the graph of $f(x) = x^2$ and the tangent line to the graph at the point (1, 1).
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Find the area of the region between the following graphs if possible: 1. f(x) = x^2 - 4x + 3 and g(x) = -x^2 + 2x + 3 2. f(x) = x^2 + 2x + 1 and g(x) = 3x + 3 3. f(x) = x, y = 2 - x, y = 0 4. Find the area of the region bounded by the graph of f(x) = x^3 and the tangent line to the graph at the point (1, 1).
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Set up and evaluate the definite integral that gives the area of the region bounded by the graph of the function and the tangent line to the graph at the given point. $$f(x)=\frac{1}{x^{2}+1}, \quad\left(1, \frac{1}{2}\right)$$
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Set up and evaluate the definite integral that gives the area of the region bounded by the graph of the function and the tangent line to the graph at the given point. $$ f(x)=\frac{1}{x^{2}+1}, \quad\left(1, \frac{1}{2}\right) $$
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