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Match the following lists : |
Answer»  `"Required area "=2int_(0)^(1)X|x|dx` `=2((x^(3))/(3))_(0)^(1)=(2)/(3)` b.  `"Required area "=int_(0)^(2)[(x+2)]-(x^(2))]dx=[(x^(2))/(2)+2x-(x^(3))/(3)]_(0)^(2)` `=2+4-(8)/(3)=(10)/(3)` sq. units. c. `"Reqd. area "=int_(0)^(1)(sqrt(x)-x)dx=[(x^(3//2))/(3//2)-(x^(2))/(2)]_(0)^(1)` `=((1)/(3//2)-(1)/(2))=(2)/(3)-(1)/(2)=(1)/(6)` sq. units.  d. `y=4" meet the parabola "y^(2)=x" at "A" is "(16,4)`  Required area= Area of rectangle OMAC-Area OMA `=4xx16-int_(0)^(16)sqrt(x)dx=64-|(x^(3//2))/(3//2)|_(0)^(16)` `=64-(2)/(3)(4)^(3)` `=64-(128)/(3)=(64)/(3)` sq. units. |
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