Mathematics

# If $3+2\displaystyle\int _{ 0 }^{ 1 }{ { x }^{ 2 }{ e }^{ -x^{ 2 } } } dx=\displaystyle\int _{ 0 }^{ 1 }{ { e }^{ -x^{ 2 } } } dx$ then the value of $\beta$ is

$\dfrac{1}{e}$

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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 $\displaystyle \int _2^3 (x^2+2x+5)\ dx$

1 Verified Answer | Published on 17th 09, 2020

Q2 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. $\displaystyle \frac{1}{2}x^{2}\sec^{-1}x-\frac{1}{2}\sqrt{x^{2}-1}+c$

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Hard
Evaluate:
$\displaystyle\int _{ 0 }^{ \pi /2 }{ \log { \left( \sin { x } \right) dx } }$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Medium
The value of $\displaystyle\int^{2\pi}_{0}\dfrac{x\sin^8x}{\sin^8x+\cos^8x}dx$ is equal to?
• A. $2\pi$
• B. $2\pi^2$
• C. $4\pi$
• D. $\pi^2$

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