Definite Integration Question 312
Question: Area bounded by the curve $ y=x{e^{x^{2}}}, $
$ x- $ axis and the ordinates $ x=0,x=a $
Options:
A) $ \frac{{e^{a^{2}}}+1}{2} $ sq. unit
B) $ \frac{{e^{a^{2}}}-1}{2} $ sq. unit
C) $ {e^{a^{2}}}+1 $ sq. unit
D) $ {e^{a^{2}}}-1 $ sq. unit
Show Answer
Answer:
Correct Answer: B
Solution:
Required area is $ \int_0^{a}{ydx=\int_0^{a}{x{e^{x^{2}}}dx}} $
We put $ x^{2}=t\Rightarrow dx=\frac{dt}{2x} $ as $ x=0\Rightarrow t=0 $ and $ x=a\Rightarrow t=a^{2} $ , then it reduces to $ \frac{1}{2}\int_0^{a^{2}}{e^{t}dt=\frac{1}{2}[e^{t}]_0^{a^{2}}=\frac{{e^{a^{2}}}-1}{2}} $ sq. unit.
BETA
