Area of Region Between Two Curves

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Notes

Notes for Area Between 2 Curves

Questions

Find the area of the region bounded by the equations

\(\textbf{1)}\) \(f(x)=x^2+4,\,g(x)=\frac{1}{2}x+1,\,x=0 \, x=3\)


\(\textbf{2)}\) \(f(x)=\sqrt{x},\,g(x)=x \)


\(\textbf{3)}\) \(f(x)=2x+3,\,g(x)=x^2-4x+4,\,x=1,\,x=3\)


\(\textbf{4)}\) \(f(x)=|x|,\,g(x)=\frac{1}{x},\,x=5\)


\(\textbf{5)}\) \(x=y^2,\,x=y+3\)


\(\textbf{6)}\) \(x=2y+4,\,x=y^2 ,\, f(x)=1,\,g(x)=3\)


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In Summary

We use integrals to find the area of a region between two curves because it is a useful tool for solving problems in a variety of fields, including physics, engineering, and economics.

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