JEE Mains · Maths · STD 12 - 7.2 definite integral
If \(\int_0^1 \frac{1}{\sqrt{3+x}+\sqrt{1+x}} d x=a+b \sqrt{2}+c \sqrt{3}\), where \(a, b, c\) are rational numbers, then \(2 a+3 b-4 c\) is equal to :
- A \(4\)
- B \(10\)
- C \(7\)
- D \(8\)
Answer & Solution
Correct Answer
(D) \(8\)
Step-by-step Solution
Detailed explanation
\( \int_0^1 \frac{1}{\sqrt{3+x}+\sqrt{1+x}} d x=\int_0^1 \frac{\sqrt{3+x}-\sqrt{1+x}}{(3+x)-(1+x)} d x \) \( \frac{1}{2}\left[\int_0^1 \sqrt{3+x} d x-\int_0^1(\sqrt{1+x}) d x\right]\)…
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