InterviewSolution
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InterviewSolution
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इन समाकलनो का मान कीजिएः `int_(0)^(1) (1)/(sqrt(1+x)-sqrt(x))dx` |
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Answer» `underset(0)overset(1)int (1)/(sqrt(1+x)-sqrt(x))dx` `=underset(0)overset(1)int((1)/(sqrt(1+x)-sqrtx)xx(sqrt(1+x)+sqrtx)/(sqrt(1+x)+sqrtx))dx` `=underset(0)overset(1)int (sqrt(1+x)+sqrtx)/((1+x)-x)dx` `=underset(0)overset(1)int (sqrt(1+x)+sqrtx)dx` `=[2/3(1+x)^(3//2)-2/3x^(3//2)]_(0)^(1)` `=[2/3(1+1)^(3//2)-2/3(1)^(3//2)] -[2/3(1+0)^(3//2)-2/3(0)^(3//2)]` `=2/3(2)^(3//2)-2/3-2/3=2/3[2sqrt2-1-1]` `=2/3(2sqrt2-2)=4/3(sqrt2-1)` |
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