Integrals — Class 12 Maths Solution

ncert exercise SA NCERT,ex.7.1,Q.21,Page 299
Question

The anti derivative of $\left( {\sqrt x + \cfrac{1}{{\sqrt x }}} \right)$ equals

  • (a) $\cfrac{1}{3}{x^{1/3}} + 2{x^{1/2}} + C$
  • (b) $\cfrac{2}{3}{x^{2/3}} + \cfrac{1}{2}{x^{1/2}} + C$
  • (c) $\cfrac{2}{3}{x^{3/2}} + 2{x^{1/2}} + C$
  • (d) $\cfrac{3}{2}{x^{3/2}} + \cfrac{1}{2}{x^{1/2}} + C$
Step-by-step Solution

Option c is correct
Let $I = \int {\left( {\sqrt x + \cfrac{1}{{\sqrt x }}} \right)dx} = \int {\left( {{x^{1/2}} + {x^{ - 1/2}}} \right)dx}$

$= \cfrac{2}{3}{x^{3/2}} + 2{x^{1/2}} + C$

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NCERT & Exemplar solution for CBSE Class 12 Mathematics, Integrals. Curated by Sachin Sharma. Free for all students.