Mathematics

# If $I=\int_{0}^{\dfrac{\pi}{2}} \dfrac{\sin^{3} x. \cos x}{\sin^{4} x+ \cos^{4} x} dx$ then $I=$

$\dfrac{\pi}{8}$

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Single Correct Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 86

#### Realted Questions

Q1 Subjective Medium
Prove that $\displaystyle \int \frac{(x^{2}+1)dx}{(x^{2}+2)(2x^{2}+1)}=\frac{1}{3\sqrt{(2)}}\left \{ \tan ^{-1}\frac{x}{\sqrt{(2)}} +\tan ^{-1} x\sqrt{2}\right \}.$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
Suppose for every integer $n, . \displaystyle \int_{n}^{n+1} f(x)dx=n^{2}$ The value of $\displaystyle \int_{-2}^{4} f(x)dx$ is :
• A. $16$
• B. $14$
• C. $21$
• D. $19$

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Hard
Evaluate: $\displaystyle \int_{0}^{\pi} \dfrac {x}{a^{2} \cos^{2}x + b^{2}\sin^{2}x} dx$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Medium
Integrate :$\dfrac{1}{1-\cot x}$
• A. $\dfrac {1}{2}\log |\sin x+\cos x|-\dfrac {1}{2}x+C$
• B. $-\dfrac {1}{2}\log |\sin x+\cos x|-\dfrac {1}{2}x+C$
• C. $-\dfrac {1}{2}\log |\sin x+\cos x|+\dfrac {1}{2}x+C$
• D. $\dfrac {1}{2}\log |\sin x-\cos x|+\dfrac {1}{2}x+C$

Integrate: $\sqrt {\left( {1 + \sin 2x} \right)}$ with respect to $x$.