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प्रश्न
If `int(2x^(1/2))/(x^2) dx = k . 2^(1/x) + C`, then k is equal to ______.
पर्याय
`(-1)/(log 2)`
− log 2
−1
`1/2`
MCQ
रिकाम्या जागा भरा
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उत्तर
If `int(2x^(1/2))/(x^2) dx = k . 2^(1/x) + C`, then k is equal to `bbunderline((-1)/(log 2))`.
Explanation:
`int(2x^(1/2))/(x^2) dx = k . 2^(1/x) + C ...(1)`
Put `1/x = t`
`(-1)/x dx = dt`
`dx = -x^2 dt`
= `int(2^t)/(x^2) (-x^2) dt`
= `-int 2^t dt`
= `(-2^t)/(log 2) + C`
Given, `int(2x^(1/2))/(x^2) dx = k . 2^(1/x) + C`
`(-2^(1/x))/(log 2) + C = K . 2^(1/x) + C`
Hence, K = `(-1)/(log 2)`
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