NIELIT 2016 MAR Scientist C - Section B: 11

Question

$\displaystyle \int_{0}^{\dfrac{\pi}{2}} \sin^{7}\theta \cos ^{4} \theta d\theta=?$

• A. $16/1155$
• B. $16/385$
• C. $16\pi/385$
• D. $8\pi/385$

Answer 1

option A will be correct

 integration of  sin^m * cos^n dx

if(m & n both are even integers)

then [(m- 1)(m -3)(m-5)....1(n -1)(n -3)(n -5)...1/(n+m)(n+ m -2)(n +m -4)...1]*pie/2

else  [(m- 1)(m -3)(m-5)....1(n -1)(n -3)(n -5)...1/(n+m)(n+ m -2)(n +m -4)...1]* 1