Mathematics

# Value of the integral $\displaystyle \int _{ 0 }^{ \pi /2 }{ \sin ^{ 3 }{ x } } { \left( 1-\cos { x } \right) }^{ 11 }dx$ is

$-\dfrac {15}{13}$

Its FREE, you're just one step away

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

#### Realted Questions

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

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
If $\displaystyle I = \int \frac {x^8}{\sqrt {1 + x^3}} dx$, then $I$ equals
• A. $\displaystyle \frac {2}{3} \sqrt {1 + x^3} \left [ \frac {1}{5} (1 + x^3)^2 + \frac {2}{3} (1 + x^3) + 1 \right ] + C$
• B. $\displaystyle \frac {2}{3} \sqrt {1 + x^3} \left [ \frac {1}{5} x^6 + \frac {4}{15} x^3 + \frac {8}{15} \right ] + C$
• C. None of these
• D. $\displaystyle \frac {2}{45} \sqrt {1 + x^3} (3x^6 - 4x^3 + 8) + C$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium
A curve is represented parametrically by the equation $x=e^t \cos t$ and $y=e^t \sin t$, where $t$ is a parameter. Then,

If $F(t)=\int (x+y)dt$, then the value of $F\left (\displaystyle \frac {\pi}{2}\right )-F(0)$ is
• A. $1$
• B. $-1$
• C. $0$
• D. $e^{\tfrac{\pi}{2}}$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
Solve $\displaystyle\int \dfrac{x}{{{{\left( {x + 1} \right)}^2}}}dx$

1 Verified Answer | Published on 17th 09, 2020

Q5 Single Correct Hard
The value of $\displaystyle \lim_{n \rightarrow \infty} \sqrt{\dfrac{9(i-1)}{n}} \cdot \dfrac{9}{n} = ?$
• A. $\int_0^9 \sqrt{x}^3 dx$
• B. $\int_0^9 \sqrt{9x} dx$
• C. $\int_1^9 \sqrt{x} dx$
• D. $\int_0^9 \sqrt{x} dx$