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CBSE Class 12 Math 2012 Solved Paper

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Question : 1 of 29
Marks: +1, -0
Evaluate ∫ 1 - x x\sqrt{x} dx
Solution:  
∫ 1 - x x\sqrt{x} dx
= ∫ (x−x3/2)(\sqrt{x}-x^{3/2}) dx
= ∫ (x1/2−x3/2)(x^{1/2}-x^{3/2}) dx
= x3/232\frac{x^{3/2}}{\frac{3}{2}}- x5/252\frac{x^{5/2}}{\frac{5}{2}} + c
= 23x3/2−23x5/2\frac{2}{3}x^{3/2}-\frac{2}{3}x^{5/2} + c
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