InterviewSolution
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InterviewSolution
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Evaluate the following definite integral: `int_1^4(x^2+x)/(sqrt(2x+1))dx` |
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Answer» Integrating by parts, taking `(x^(2)+x)` as the first function and `(1)/(sqrt(2x+1))` as the second function, we get `int_(2)^(4)((x^(2)+x))/(sqrt(2x+1))dx=[(x^(2)+x)*sqrt(2x+1)]_(2)^(4)-int_(2)^(4)(2x+1)*sqrt(2x+1)dx` `=(60-6sqrt(5))-int_(2)^(4)(2x+1)^(3//2)dx` `=(60-6sqrt(5))-(1)/(5)*[(2x+1)^(5//2)]_(2)^(4)` `=(60-6sqrt(5))-((243)/(5)-5sqrt(5))` `=((57)/(5)-sqrt(5))=sqrt((57-5sqrt(5))/(5))`. |
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