A) \[\frac{16}{5}\]
B) \[\frac{21}{5}\]
C) \[\frac{7}{10}\]
D) \[\frac{27}{10}\]
Correct Answer: A
Solution :
\[I=\int_{{}}^{{}}{\frac{dx}{{{\cos }^{3}}x{{\sin }^{\frac{1}{2}}}x{{\cos }^{\frac{1}{2}}}x}=\frac{1}{2}\int_{{}}^{{}}{\frac{({{\tan }^{2}}x+1){{\sec }^{2}}x}{{{(\tan x)}^{\frac{1}{2}}}}}}dx\] \[\tan x=t\]\[I=\frac{1}{2}\int_{{}}^{{}}{{{t}^{\frac{3}{2}}}}dt+\frac{1}{2}\int_{{}}^{{}}{{{t}^{\frac{1}{2}}}}dt\] \[=\frac{{{t}^{\frac{5}{2}}}}{5}+{{t}^{1/2}}dt+\frac{1}{2}\int_{{}}^{{}}{{{t}^{-\frac{1}{2}}}}dt\] \[=\frac{{{t}^{\frac{5}{2}}}}{5}+{{t}^{1/2}}+c=\frac{{{(\tan x)}^{\frac{5}{2}}}}{5}+{{(\tan x)}^{1/2}}\] \[A=\frac{1}{2},B=\frac{5}{2},C=\frac{1}{5}\] \[A+B+C=\frac{16}{5}\]
You need to login to perform this action.
You will be redirected in
3 sec
