A) \[A=\frac{1}{9072},p=\left( \frac{{{x}^{7}}-6}{{{x}^{7}}} \right)\]
B) \[A=\frac{1}{54432},p=\left( \frac{{{x}^{7}}-6}{{{x}^{7}}} \right)\]
C) \[A=\frac{1}{54432},p=\left( \frac{{{x}^{7}}}{{{x}^{7}}-6} \right)\]
D) \[A=\frac{1}{9072},p={{\left( \frac{{{x}^{7}}-6}{{{x}^{7}}} \right)}^{-1}}\]
Correct Answer: B
Solution :
| [b] Let \[I=\int{\frac{dx}{{{x}^{29}}\left( 1-\frac{6}{{{x}^{7}}} \right)}}\] |
| Put \[1-\frac{6}{{{x}^{7}}}=p\Rightarrow \frac{42}{{{x}^{8}}}dx=dp\] and \[{{x}^{7}}=\frac{6}{1-p}\] |
| \[\therefore I=\frac{1}{42}\int{\frac{{{(1-p)}^{3}}}{{{(6)}^{3}}p}dp}\] |
| \[=\frac{1}{(42)(216)}\int{\frac{1-{{p}^{3}}-3p+3{{p}^{2}}}{p}dp}\] |
| \[=\frac{1}{9072}\int{\left( \frac{1}{p}-{{p}^{2}}-3+3p \right)dp}\] |
| \[=\frac{1}{9072}\left( \log p-\frac{{{p}^{3}}}{3}-3p+\frac{3}{2}{{p}^{2}} \right)+c\] |
| \[=\frac{1}{54432}(6l\,np-2{{p}^{3}}-18p+9{{p}^{2}})+c\] |
| \[=\frac{1}{54432}(l\,n{{p}^{6}}+9{{p}^{2}}-2{{p}^{3}}-18p)+c\] |
| \[A=\frac{1}{54432},p=\left( \frac{{{x}^{7}}-6}{{{x}^{7}}} \right)\] |
You need to login to perform this action.
You will be redirected in
3 sec
