Mathematics

# Let ${ I }_{ 1 }=\displaystyle \int _{ 0 }^{ 1 }{ { \left( 1-{ x }^{ 50 } \right) }^{ 100 }dx }$ and ${ I }_{ 2 }=\displaystyle \int _{ 0 }^{ 1 }{ { \left( 1-{ x }^{ 50 } \right) }^{ 101 }dx }$, then $\dfrac { { I }_{ 1 } }{ { I }_{ 2 } } =$

$\dfrac {5051}{5050}$

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Single Correct Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84

#### Realted Questions

Q1 Subjective Medium
Evaluate: $\displaystyle\int { \tan ^{ 3 }{ x } } dx$

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Medium
Solve $\displaystyle\int\limits_b^a {\frac{x}{{\sqrt {{a^2} + {x^2}} }}dx}$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium
If $\displaystyle\int { \sqrt { 1+\sin { x } } \cdot f\left( x \right) dx } =\dfrac { 2 }{ 3 } { \left( 1+\sin { x } \right) }^{ { 3 }/{ 2 } }+C$, then $f\left( x \right)$ is equal to
• A. $\sin { x }$
• B. $\tan { x }$
• C. $1$
• D. $\cos { x }$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Medium
The value of integratin $\displaystyle \int x\sec^{-1}xdx$ is
• A. $\dfrac{1}{2}x^{2}\sec^{-1}x+\displaystyle \frac{1}{2}\sqrt{x^{2}-1}+c$
• B. $x^{2}\sec^{2}x+\displaystyle \frac{1}{2}\sqrt{x^{2}-1}+c$
• C. $x^{2}\sec^{2}x-\dfrac{1}{2}\sqrt{x^{2}-1}+c$
• D. $\displaystyle \frac{1}{2}x^{2}\sec^{-1}x-\frac{1}{2}\sqrt{x^{2}-1}+c$

$\int_{}^{} {\frac{{ - 1}}{{\sqrt {1 - {x^2}} }}dx}$