Question Id : 18024 |
Context : JEE Main 2026 (23 January Evening Shift)
Let $I(x) = \int \dfrac{3dx}{(4x+6)\sqrt{4x^2 + 8x + 3}}$ and
$I(0) = \dfrac{\sqrt{3}}{4} + 20$. If $I\left(\dfrac{1}{2}\right) = \dfrac{a\sqrt{2}}{b} + c$, where $a,b,c \in \mathbb{N}$, $\gcd(a,b)=1$, then $a + b + c$ is equal to:
🎥 Video solution / Text Solution of this question is given below:
Let $4x+6 = \dfrac{1}{t}$
$I(x) = \frac{3}{4}\sqrt{\frac{4x+2}{4x+6}} + c$
$I(0) = \frac{\sqrt{3}}{4} + c \Rightarrow c = 20$