SATHEE: Area Question 15

Area Question 15

Question 15

$\int_{- 1}^{1} g^{'} (x) d x$ is equal to (a) $2 g (- 1)$ (b) 0 (c) $- 2 g (1)$ (d) $2 g (1)$

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Solution:

Required area

$\begin{aligned} = \int_{0}^{1} (1 + \sqrt{x}) d x + \int_{1}^{2} (3 - x) d x - \int_{0}^{2} \frac{x^{2}}{4} d x & X^{'} \to_{(0, 0)}^{(0, 3)} \end{aligned}$

$\begin{aligned} = 1 + \frac{2}{3} + 6 - 2 - 3 + \frac{1}{2} - \frac{8}{12} & = \frac{5}{3} + \frac{3}{2} - \frac{2}{3} = 1 + \frac{3}{2} = \frac{5}{2} sq units \end{aligned}$

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