Integral Calculus Question 440
Question: For which of the following functions, the substitution $ x^{2}=t $ is applicable
Options:
A) $ \int_{{}}^{{}}{x^{6}{{\tan }^{-1}}x^{3}}\ dx $
B) $ \int_{{}}^{{}}{{{\tan }^{-1}}( \frac{2x}{1-x^{2}} )\ dx} $
C) $ \int_{{}}^{{}}{x^{3}\cos x^{2}\ dx} $
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
$ x^{2}=t $ is applicable for $ \int_{{}}^{{}}{x^{3}\cos x^{2},dx} $ $ =\frac{1}{2}\int_{{}}^{{}}{t\cos t,dt}=\frac{1}{2}(t\sin t-\int_{{}}^{{}}{\sin t,dt+c)} $ $ =\frac{1}{2}(t\sin t+\cos t+c)=\frac{1}{2}(x^{2}\sin x^{2}+\cos x^{2}+c). $
BETA
