Area Question 15
Question 15
- $\int_{-1}^{1} g^{\prime}(x) d x$ is equal to (a) $2 g(-1)$ (b) 0 (c) $-2 g(1)$ (d) $2 g(1)$
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Solution:
- Required area
$$ \begin{aligned} & =\int_{0}^{1}(1+\sqrt{x}) d x+\int_{1}^{2}(3-x) d x-\int_{0}^{2} \frac{x^{2}}{4} d x \ & X^{\prime} \xrightarrow[(0,0)]{(0,3)} \end{aligned} $$
$$ \begin{aligned} & =1+\frac{2}{3}+6-2-3+\frac{1}{2}-\frac{8}{12} \ & =\frac{5}{3}+\frac{3}{2}-\frac{2}{3}=1+\frac{3}{2}=\frac{5}{2} \text { sq units } \end{aligned} $$
