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CBSE Class 12-commerce Answered

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Asked by morninggood0966 | 29 Feb, 2024, 04:06: PM
answered-by-expert Expert Answer

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Let I = I1 + I2

where I1 and I2 are defined as

img    and  img

Let us solve the first integration I1 .

Let  u = 4√x = x1/4 ;  

du = (1/4) x-3/4 dx = (1/4) u-3 dx

dx = 4 u3 du

Hence the first integration I1 is

img

we can write the integrand function as

img

img

img

img

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Let us solve the second integration

img

img

img

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where I3 is

img

Let v = √x  ;

dv = dx/ ( 2 √x ) ;

dx = 2 u du

img

img

I3 = 2 u - 2 log(1+u )

I3  = 2 √x - ln( 1 + √x )2

Hence the complete integration is

img

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Answered by Thiyagarajan K | 01 Mar, 2024, 05:14: PM
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