Mathematics

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


ANSWER

$$-\dfrac {15}{13}$$


View Full Answer

Its FREE, you're just one step away


Single Correct Medium Published on 17th 09, 2020
Next Question
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84
Enroll Now For FREE

Realted Questions

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

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
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. $$\displaystyle \frac {2}{45} \sqrt {1 + x^3} (3x^6 - 4x^3 + 8) + C$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
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. $$e^{\tfrac{\pi}{2}}$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

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

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
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. $$\int_0^9 \sqrt{x} dx$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer