Mathematics
##### ASSERTION

$\displaystyle \int \frac{dx}{x^{3}\sqrt{1+x^{4}}}=-\frac{1}{2}\sqrt{1+\frac{1}{x^{^{4}}}}+C.$

##### REASON

For integration by parts, we have to follow ILATE rule.

##### ANSWER

Assertion is True, Reason is True; Reason is NOT a correct explanation for Assertion

##### SOLUTION
$\displaystyle I=\int \frac{dx}{x^{3}\sqrt{1+x^{4}}}$

$\displaystyle =\int \frac{dx}{x^{5}\sqrt{\frac{1}{x^{^{4}}}}+1}$

Put $\displaystyle \frac{1}{x^{4}}+1=t$
$\displaystyle dt=\frac{-4}{x^{5}}dx$

$\displaystyle \therefore I=-\frac{1}{4}\int \frac{dt}{\sqrt{t}}$

$\displaystyle =-\frac{1}{2}\sqrt{t}+C$
$\displaystyle =-\frac{1}{2}\sqrt{1+\frac{1}{x^{4}}}+C$
Hence, statement 1 is true.
Also, for integration by parts, we need to follow ILATE.
Thus, both the statements are true but statement 2 is not a correct explanation of statement 1.

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Assertion & Reason Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84

#### Realted Questions

Q1 Single Correct Medium
Solve :
$\displaystyle \int x.(x^{x})^{x}(2\log x+1)dx$
• A. $x^{(x^{x})}+c$
• B. $x^{x}.\log x+c$
• C. does not exist
• D. $(x^{x})^{x}+c$

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1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
Evaluate : $\displaystyle\int \frac{\cos \sqrt{x}}{\sqrt{x}}dx.$
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• B. $\displaystyle 2\sin x.$
• C. $\displaystyle 2\sin \sqrt{x}/3.$
• D. $\displaystyle 2\sin \sqrt{x}.$

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Q3 Subjective Medium
Evaluate $\int \frac{x- \sin x}{1- \cos x} dx$.

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Q4 Subjective Medium
$\int \sin x \log (\cos x)dx$

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Q5 Passage Medium
Let $\displaystyle f\left ( x \right )=\frac{\sin 2x \cdot \sin \left ( \dfrac{\pi }{2}\cos x \right )}{2x-\pi }$

Then answer the following question.

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020