Definite Integration Question 181
Question: Let f(x) be a continuous function such that the area bounded by the curve y = f(x), x-axis and the lines x = 0 and x = a is $ \frac{a^{2}}{2}+\frac{a}{2}\sin a+\frac{\pi }{2}\cos a $ , then $ f( \frac{\pi }{2} )= $
Options:
A) 1
B) $ \frac{1}{2} $
C) $ \frac{1}{3} $
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
[b] We have, $ \int\limits_0^{a}{f(x)dx=\frac{a^{2}}{2}+\frac{a}{2}\sin a+\frac{\pi }{2}\cos a} $
Differentiating w.r.t. a, we get $ f(a)=a+\frac{1}{2}(\sin a+a\cos a)-\frac{\pi }{2}\sin a $ Put $ a=\frac{\pi }{2};f( \frac{\pi }{2} )=\frac{\pi }{2}+\frac{1}{2}-\frac{\pi }{2}=\frac{1}{2} $
BETA
