Mathematics
##### ASSERTION

$\displaystyle \int_{-\pi /4}^{\pi /4}x^{3}\sin ^{4}xdx\neq 0$

##### REASON

$\displaystyle \int_{-a}^{a}f\left ( x \right )dx=0$ if $f\left ( -x \right )=-f\left ( x \right )$

Assertion is incorrect but Reason is correct

##### SOLUTION
For an odd function $f(-x)=-f(x)$ and

If $f(x)$ is an odd function then $\int_{-a}^{a}f(x)dx=0$.

Given $f(x)=x^3sin^4x$ is an odd function hence,

$\int_{-\pi/4}^{\pi/4}x^3sin^4dx=0$.

So assertion is incorrect but reason is correct.

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Assertion & Reason Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 86

#### Realted Questions

Q1 One Word Hard
$\displaystyle \int \frac{\cos x}{5-3\cos x}dx=-\frac{1}{3}x+\frac{k}{6}\tan ^{-1}\left [ 2\tan \frac{x}{2} \right ].$ Find the value of $k$.

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
$\displaystyle \int e^{tan^{-1}x}\left[\frac{1+x+x^{2}}{1+x^{2}}\right]dx=$
• A. $\displaystyle x^{2}e^{\tan^{-1}x}+c$
• B. $\displaystyle e^{\tan^{-1}x}+c$
• C. $\displaystyle \frac{1}{2}e^{\tan^{-1}x}+c$
• D. $\displaystyle x e^{\tan^{-1}x}+c$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium
$n\overset{Lt}{\rightarrow}\infty [\displaystyle \frac{1}{1-n^{2}}+\frac{2}{1-n^{2}}+\ldots+\frac{n}{1-n^{2}}]=$
• A.
• B. 1/2
• C. 1
• D. -1/2

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
Integrate:
$\displaystyle \int \left(4\sin x- \dfrac{3}{x}2x^{3}+4 \right)$

Evaluate $\int \dfrac{e^x-e^{-x}}{e^x+e^{-x}}dx$