Integrals
NCERT Class 12
CBSE
Grade 12
Question:
The anti-derivative of $\left(\sqrt{x} + \dfrac{1}{\sqrt{x}}\right)$ is equal to:
(a) $\dfrac{2}{3} x^{3/2} + 2 x^{1/2} + C$
(b) $\dfrac{1}{3} x^{3/2} + \dfrac{1}{2} x^{1/2} + C$
(c) $\dfrac{3}{2} x^{3/2} + \dfrac{1}{2} x^{1/2} + C$
(d) $\dfrac{2}{3} x^{3/2} + \dfrac{1}{2} x^{1/2} + C$
Step-by-Step Solution
$\int (x^{1/2} + x^{-1/2}) dx = \dfrac{2}{3} x^{3/2} + 2 x^{1/2} + C$. [1.0 Mark]
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🎯 Official CBSE Marking Scheme:
Evaluating anti-derivative $= (2/3)x^{3/2} + 2x^{1/2} + C$: 1.0 Mark
Correct Answer: $\dfrac{2}{3} x^{3/2} + 2 x^{1/2} + C$
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