JEE Main 2017 · 9 Apr · Shift 1 · Mathematics Q75

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MathematicsSingle correct+4 / -1Question 75 of 90

If $\displaystyle\int_1^2\frac{dx}{(x^2-2x+4)^{3/2}}=\frac k{k+5}$ , then k is equal to :

Answer and worked solution

Official answer: A

With $u=x-1$ : $\displaystyle\int_0^1\frac{du}{(u^2+3)^{3/2}}=\left[\frac u{3\sqrt{u^2+3}}\right]_0^1=\frac16$ . So $\frac k{k+5}=\frac16$ and $k=1$ .

Topics:Fundamental theorem of calculus Standard integrals

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JEE Main 2017 · 9 Apr · Shift 1, Mathematics question 75