Find the area of the region bounded by $\mathrm{f}(x) = e^x - e^{-x}$ the $x$-axis, the line \(x

Question

Find the area of the region bounded by $\mathrm{f}(x) = e^x - e^{-x}$ the $x$-axis, the line $x = -1$ and the line $x = 1$. $\mathrm{f}(x) = \frac{1}{x-1} + 1$, the $x$-axis, the line $x = -1$ and the line $x = 0.5$. $y = \cos 2x + 1$, the $x$-axis, the line $x = 0$ and the line $x = \frac{\pi}{2}$. $y = x(x+1)(x-2)$ and the $x$-axis. $y = |2x - 1|$, the $x$-axis, the line $x = -1$ and the line $x = 2$. $y = |2x| - 1$, the $x$-axis, the line $x = -1$ and the line $x = 2$.

Accepted Answer

(i) $2(\mathrm e+\mathrm e^{-1}-2)$. (ii) $\frac{1}{2}$. (iii) $\frac{\pi}{2}$. (iv) $\frac{37}{12}$. (v) $\frac{9}{2}$. (vi) $3$.

Applications of Integration - Area bounded by 2 curves

Applications of Integration - Area bounded by 2 curves

Solution:

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