Let I = 2 x dx Let x = t xdx = dt I = = - 1 ( 2 ) + C = - 1 ( 2 ) + C

Integrals — Class 12 Maths Solution

ncert misc SA NCERT Misc.,Q.9,Page.352

Question

$\cfrac{{\cos x}}{{\sqrt {4 - {{\sin }^2}x} }}$

Step-by-step Solution

Let $I = \int {\cfrac{{\cos x}}{{\sqrt {4 - {{\sin }^2}x} }}} dx$

Let $\sin x = t$ $\Rightarrow$ $\cos xdx = dt$

$\therefore$ $I = \int {\cfrac{{dt}}{{\sqrt {4 - {t^2}} }} = {{\sin }^{ - 1}}\left( {\cfrac{t}{2}} \right)} + C = {\sin ^{ - 1}}\left( {\cfrac{{\sin x}}{2}} \right) + C$

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