Answer is: option1
2Solution:
Let \( u = 1 + x \Rightarrow du = dx \)
When \( x = 0 \), \( u = 1 \)
When \( x = 3 \), \( u = 4 \)
Now the integral becomes:
\[ \int_1^4 \frac{1}{\sqrt{u}} \, du = \int_1^4 u^{-\frac{1}{2}} \, du \]
\[ \int u^{-\frac{1}{2}} \, du = 2u^{\frac{1}{2}} + C \]
Evaluate the definite integral:
\[ 2u^{\frac{1}{2}} \Big|_1^4 = 2(\sqrt{4}) - 2(\sqrt{1}) = 2(2) - 2(1) = 4 - 2 = 2 \]
Correct Answer is (A) ie., 2