First slide

Area of bounded Regions

Question

$The maximum possible area bounded by the curves y = \cos x, y = x + 1, y = 0 is$

Moderate

A

$\frac{3}{2}$
B

$\frac{2}{3}$
C

$\frac{1}{2}$
D

$\frac{5}{2}$

Solution

$\begin{array}{l} Given curves are y = \cos x, y = x + 1, y = 0 \\ Required area, A = \int_{0}^{\frac{π}{2}} \cos x d x + \frac{1}{2} \times 1 \times 1 \\ = (\sin x)_{0}^{\frac{π}{2}} + \frac{1}{2} \\ = 1 - 0 + \frac{1}{2} \\ = \frac{3}{2} sq.units \end{array}$

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