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Joint Entrance Examination
Mathematics
Area Under Curves
Question 49
Question 49 of 230
Medium
MCQ
The area (in sq. units) of the region, given by the set \[\{ (x,y) \in R \times R|x \ge 0,2{x^2} \le y \le 4 - 2x\} \] is :
A
8
3
\frac{8}{3}
3
8
B
17
3
\frac{17}{3}
3
17
C
13
3
\frac{13}{3}
3
13
D
7
3
\frac{7}{3}
3
7
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Official solution
Required area = \[\left. {\int\limits_0^1 {\left( {4 - 2x - 2{x^2}} \right)dx = 4x - {x^2} - {{2{x^3}} \over 3}} } \right|_0^1\] \[ = 4 - 1 - {2 \over 3} = {7 \over 3}\]
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