InterviewSolution
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InterviewSolution
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फलन `x^(3)sqrt((x^(2) - 4))` का x के सापेक्ष समाकलन कीजिये । |
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Answer» माना `I = intx^(3)sqrt((x^(2) - 4))dx " ".....(1)` माना `x^(2)- 4 = trArr x^(2) = (t +4)` तथा `2x dx = dt rArr x dx = (1)/(2) dt` अतः समीकरण (1 ) से `I = int x^(2) xsqrt((x^(2) - 4))dx` ` = (1)/(2)int(t + 4)t^(1//2) +dt = (1)/(2)int[t^(3//2) + 4t^(1//2)]dt` ` = (1)/(2)[(2)/(5) t^(5//2) +(4xx2)/(3) t^(3//2)] = (1)/(5) t^(5//2) +(4)/(3) t^(3//2)` ` = (1)/(5)(x^(2) - 4)^(5//2)+(4)/(3)(x^(2) - 4)^(3//2)` |
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