Definite Integration Question 497
Question: $ \int_0^{a}{x^{2}\sin x^{3}dx} $ equals
[RPET 1996]
Options:
A) $ (1-\cos a^{3}) $
B) $ 3(1-\cos a^{3}) $
C) $ -\frac{1}{3}(1-\cos a^{3}) $
D) $ \frac{1}{3}(1-\cos a^{3}) $
Show Answer
Answer:
Correct Answer: D
Solution:
$ I=\int_0^{a}{x^{2}\sin x^{3}dx} $ ; Put $ x^{3}=t\Rightarrow x^{2}dx=\frac{dt}{3} $
$ \therefore I=\frac{1}{3}\int_0^{a^{3}}{\sin tdt}=-\frac{1}{3}[\cos t]_0^{a^{3}}=-\frac{1}{3}[\cos a^{3}-1] $
$ =\frac{1}{3}[1-\cos a^{3}] $ .
BETA
