Definite Integration Question 183
Question: If $ c_1=y=\frac{1}{1+x^{2}} $ and $ c_2=y=\frac{x^{2}}{2} $ be two curves lying in XY-plane, then
Options:
A) Area bounded by curve $ y=\frac{1}{1+x^{2}} $ and $ y=0 $ is $ \frac{\pi }{2} $
B) Area bounded by $ c_1 $ and $ c_2 $ is $ \frac{\pi }{2}-1 $
C) Area bounded by $ c_1 $ and $ c_2 $ is $ 1-\frac{\pi }{2} $
D) Area bounded by curve $ y=\frac{1}{1+x^{2}} $ and x-axis is $ \frac{\pi }{2} $
Show Answer
Answer:
Correct Answer: B
Solution:
[b] Area bounded by $ y=\frac{1}{1+x^{2}} $ and x - axis is $ \int _{-\infty }^{\infty }{\frac{1}{1+x^{2}}dx=\pi } $
Area bounded by two curves is $ \int _{-1}^{1}{( \frac{1}{1+x^{2}}-\frac{x^{2}}{2} )dx=\frac{\pi }{2}-1} $
BETA
