Mathematics

$$\displaystyle \int_{0}^{1}x\left ( 1-x \right )^{4}dx= \frac{1}{C}$$, then $$C=?$$


ANSWER

30


SOLUTION
Let $$\displaystyle I=\int _{ 0 }^{ 1 } x\left( 1-x \right) ^{ 4 }dx$$
Using $$\int _{ a }^{ b }{ f\left( x \right) dx } =\int _{ a }^{ b }{ f\left( a+b-x \right) dx } $$
$$\displaystyle \therefore I=\int _{ 0 }^{ 1 } \left( 1-x \right) x^{ 4 }dx=\int _{ 0 }^{ 1 } \left( x^{ 4 }-x^{ 5 } \right) dx=\frac { 1 }{ 5 } -\frac { 1 }{ 6 } =\frac { 1 }{ 30 } $$
View Full Answer

Its FREE, you're just one step away


One Word Medium Published on 17th 09, 2020
Next Question
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 105
Enroll Now For FREE

Realted Questions

Q1 Subjective Medium
Evaluate
$$\displaystyle\int { \dfrac { { x }^{ 3 }+{ 4x }^{ 2 }-7x+5 }{ x+2 }  } dx$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q2 Single Correct Medium
If $$f(x)$$ is an even function, then $$\displaystyle \int_{0}^{x}f(t)\, dt$$ is
  • A. Even function
  • B. Neither even nor odd
  • C. None of the above
  • D. Odd function

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q3 Subjective Hard
Prove that $$\displaystyle \int _{\frac{\pi}{3}}^{\frac{\pi}{6}} \dfrac{dx}{1+\sqrt{\cot\, x}} =\int _{\frac{\pi}{3}}^{\frac{\pi}{6}} \dfrac{dx}{1+\sqrt{\tan\, x}}$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q4 Subjective Medium
$$\displaystyle \int _{ 2 }^{ 3 }{ \left( 1+2x \right)  } dx$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q5 Subjective Easy
Evaluate:
$$ \int_{}^{} {\frac{{ - 1}}{{\sqrt {1 - {x^2}} }}dx} $$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer