$\int\limits^4_1 {x} \, dx$ where...
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intlimits^4_1 {x} , dx where f(x) = x^{2} ; 1 ≤x<2 and f(x) = 3x-4; 2 ≤x<4 is (a) 7/3 (b) 10 (c) 23/3 (d) 37/3

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( int_{1}^{4} f(x) d x ) ( f(x)=int_{3 x^{2}-4}^{x^{2}} 2 leq x / 2 ) ( =int_{1}^{2} f(x) d x+int_{2}^{4} f(x) d(x) ) ( int_{1}^{2} x^{2} d x+int_{2}^{4}(3 x-4) d x ) ( Rightarrowleft[left.frac{x^{3}}{3}right|_{1} ^{2}+left[frac{3 x^{2}}{2}-4 xright]_{2}^{4}right. ) ( aleft(frac{8}{3}-frac{1}{3}right)+left(frac{3}{2}(16-4)-4(+-2)right] ) ( =frac{7}{3}+18-8 ) ( 2+frac{7}{3}+10=2 sqrt{frac{37}{3}} )
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