Mathematics

# Prove that $\displaystyle\int^1_0x(1-x)^5dx=\dfrac{1}{42}$.

##### SOLUTION

Its FREE, you're just one step away

Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 105

#### Realted Questions

Q1 Subjective Medium
Write a value of
$\int { { e }^{ \log { \sin { x } } }\cos { x } } dx$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
$I_n = \int^x_0 e^x (sin x)^n dx$ , then $\dfrac{I_3}{I_1}$ is equal to
• A. $\dfrac{1}{5}$
• B. $1$
• C. $\dfrac{2}{5}$
• D. $\dfrac{3}{5}$

1 Verified Answer | Published on 17th 09, 2020

Q3 Multiple Correct Hard
If $\displaystyle \int xe^{-5x^2} \: sin \: 4x^2 dx = Ke^{-5x^2} (A \: sin \: 4x^2 + B \: cos \: 4x^2) + C$. Then
• A. $\dfrac {1}{82}, -5, 4$
• B. $\dfrac {1}{82}, \dfrac{-1}{5}, \dfrac{-1}{4}$
• C. $\dfrac {1}{82}, 5, 4$
• D. $\dfrac {1}{82}, -5, -4$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Medium
$\displaystyle \int\frac{3}{\sqrt{9z^{2}-1}}dz=$
• A. $\displaystyle \sinh ^{ -1 }{ \left( 3z \right) }+c$
• B. $\displaystyle {\frac{1}{2}}\cosh ^{ -1 }{ \left( 3z \right) }+c$
• C. $\displaystyle {\frac{1}{2}}\sinh ^{ -1 }{ \left( 3z \right) }+c$
• D. $\displaystyle \cosh ^{ -1 }{ \left( 3z \right) } +c$

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