InterviewSolution
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InterviewSolution
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`int(sqrtx)/(sqrt(a^(3)-x^(3)))dx` का मान ज्ञात कीजिए । |
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Answer» माना `I=int(sqrtx)/(sqrt(a^(3)-x^(3)))dx=int(sqrtx)/(sqrt((a^(3//2))-(x^(3//2))))dx` `x^(3//2)=a^(3//2)t` रखने पर `rArr" "(3)/(2)x^(1//2)dx=a^(3//2)dt=sqrtx dx =(2)/(3)a^(3//2)dt` `therefore" "I=int((2//3)a^(3//2))/(sqrt((a^(3//2))^(2)-(a^(3//2)t)^(2)))` `=(2)/(3)a^(3//2)int(dt)/(a^(3//2)sqrt(1-t^(2)))` `=(2)/(3)int(dt)/(sqrt(1-t^(2)))=(2)/(3)sin^(-1)((t)/(1)+c)` `=(2)/(3)sin^(-1)((x^(3//2))/(a^(3//2)))+c" "[t=(x^(3//2))/(a^(3//2))" रखने पर "]` `=(2)/(3)sin^(-1)(sqrt((x^(3))/(a^(3))))+c` |
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