Definite Integration Question 124
Question: If $ f(x)=\int_a^{x}{t^{3}e^{t}dt,} $ then $ \frac{d}{dx}f(x)= $
[MP PET 1989]
Options:
A) $ e^{x}(x^{3}+3x^{2}) $
B) $ x^{3}e^{x} $
C) $ a^{3}e^{a} $
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
$ f(x)=\int_a^{x}{t^{3}e^{t}dt=\int_a^{0}{t^{3}.e^{t}dt+\int_0^{x}{t^{3}e^{t}dt}}} $
$ \Rightarrow \frac{df(x)}{dx}=\frac{d}{dx}( \int_a^{0}{t^{3}.e^{t}dt} )+\frac{d}{dx}( \int_0^{x}{t^{3}.e^{t}dt} )=x^{3}e^{x} $ .
BETA
