Question
If \(f(x)=2\ln(\sqrt{e^x})\) , what is the area bounded by f(x) for the interval [0, 2] on the x-axis?
The correct answer is
2
\(f(x)=2\ln(e^{x/2})=x\)
\(A=\int_0^2x\,dx=2\)
The area is 2 square units.
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Important Questions from Application of Integrals
What is the area of one of the loops between the curve y = c sin x and x-axis?
- The area enclosed between the curves $y = -x^2 + 4x$ and $y = x^2 - 2x$ is
The equation of the normal at the point (1, 1) on the curve 2y + x2 = 3 is
There are two curves in a graph. One is y = x2 and the other is y = x. Find the area enclosed between these curves.
The area enclosed between the curves y2 = x and y = |x| is:
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