Integral Calculus Question 224
Question: $ \int_{{}}^{{}}{x^{3}\sqrt{3+5x^{4}}}\ dx= $
[DSSE 1982]
Options:
A) $ {{(3+5x^{4})}^{3/2}}+c $
B) $ \frac{1}{5}{{(3+5x^{4})}^{3/2}}+c $
C) $ \frac{1}{30}{{(3+5x^{4})}^{3/2}}+c $
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
Put $ 3+5x^{4}=t\Rightarrow 20x^{3}dx=dt, $ then $ \int_{{}}^{{}}{x^{3}\sqrt{3+5x^{4}}dx}=\frac{1}{20}\int_{{}}^{{}}{{t^{1/2}}dt} $ $ =\frac{2}{3}\times \frac{1}{20}.{t^{3/2}}+c=\frac{1}{30}{{(3+5x^{4})}^{3/2}}+c. $
BETA
