Question

If `intsqrt((x - 5)/(x - 7))dx = Asqrt(x^2 - 12x + 35) + log|x| - 6 + sqrt(x^2 - 12x + 35) + C|`, then A = ______.

विकल्प

• –1

• `1/2`

• `-1/2`

• 1

Answer 1

If `intsqrt((x - 5)/(x - 7))dx = Asqrt(x^2 - 12x + 35) + log|x| - 6 + sqrt(x^2 - 12x + 35) + C|`, then A = 1.

Explanation:

Consider, I = `intsqrt((x - 5)/(x - 7))dx`

= `intsqrt(((x - 5)(x - 5))/((x - 7)(x - 5)))dx`

= `int (x - 5)/sqrt(x^2 - 12x + 35)dx`

= `1/2int (2x - 12 + 2)/sqrt(x^2 - 12x + 35)`

= `1/2int(2x - 12)/(sqrt(x^2 - 12x + 35))dx + int 1/sqrt(x^2 - 12x + 35)dx`

= `sqrt(x^2 - 12x +35) + int 1/sqrt((x^2 - 12x + 36 - 1))dx+ C`

= `sqrt(x^2 - 12x + 35) + int 1/sqrt((x - 6)^2 - 1^2)dx + C`

I = `sqrt(x^2 - 12x + 35) + log|x - 6 + sqrt(x^2 - 12x + 35)| + C`

As, I = `Asqrt(x^2 - 12x + 35) + log|x - 6 + sqrt(x^2 - 12x + 35) + C|`

Hence, A = 1