Definite Integration Question 203
Question: $ \int_0^{\pi /4}{{{\sec }^{7}}\theta {{\sin }^{3}}\theta }d\theta = $
Options:
A) $ \frac{1}{12} $
B) $ \frac{3}{12} $
C) $ \frac{5}{12} $
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
$ \int_0^{\pi /4}{{{\sec }^{7}}\theta }.{{\sin }^{3}}\theta d\theta $ = $ \int_0^{\pi /4}{\frac{{{\sin }^{3}}\theta }{{{\cos }^{3}}\theta }.{{\sec }^{4}}\theta d\theta } $
Putting $ \tan \theta =t, $ it reduces to $ \int_0^{1}{t^{3}(1+t^{2})dt} $ = $ | \frac{t^{4}}{4}+\frac{t^{6}}{6} |_0^{1}=\frac{5}{12} $ .
BETA
