Mathematics

Solve : $$ \int (1 - x) \sqrt{x}  \, dx$$


SOLUTION
$$\int (1-x)\sqrt{x}dx$$

$$\int \sqrt{x}-x^{\frac{3}{2}}dx$$

$$=\dfrac{2}{3}x^{\frac{3}{2}}-\dfrac{2}{5}x^{\frac{5}{2}}+C$$
View Full Answer

Its FREE, you're just one step away


Subjective 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:
$$\displaystyle\int^2_1\dfrac{dx}{x(x^4+1)}$$.

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q2 Subjective Medium
Evaluate the following integrals:
$$\int { \sqrt { x-{ x }^{ 2 } }  } dx$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q3 Single Correct Hard
$$\displaystyle \int \frac{\sec^{2}x dx}{\sqrt{\tan^{2} x+4}}=$$
  • A. $$\dfrac{1}{2}\ln\left ( \tan x+\sqrt{\tan^{2} x+4} \right )+C$$
  • B. $$\ln\left ( \dfrac{1}{2}\tan x+\dfrac{1}{2}\sqrt{\tan^{2} x+4} \right )+C$$
  • C. None of these
  • D. $$\ln\left ( \tan x+\sqrt{\tan^{2} x+4} \right )+C$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q4 Single Correct Hard
The value of $$\displaystyle \int \dfrac {dx}{x(x^{n} + 1)}$$ is
  • A. $$\log \left (\dfrac {x^{n} + 1}{x^{n}}\right ) + C$$
  • B. $$\dfrac {1}{n}\log \left (\dfrac {x^{n} + 1}{x^{n}} \right ) + C$$
  • C. $$\log \left (\dfrac {x^{n}}{x^{n} + 1}\right ) + C$$
  • D. $$\dfrac {1}{n} \log \left (\dfrac {x^{n}}{x^{n} + 1}\right ) + C$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q5 Single Correct Medium
If $$\displaystyle f\left ( x \right )$$ is a function of $$x$$ such that $$\displaystyle \frac{1}{\left ( 1 + x \right ) \left ( 1 + x^{2} \right )} = \frac{A}{1 + x} + \frac{f\left ( x \right )}{1 + x^{2}}$$ for all $$\displaystyle x \: \epsilon \: R$$ then $$\displaystyle f\left ( x \right )$$ is
  • A. $$\displaystyle \frac{x + 1}{2}$$
  • B. $$\displaystyle 1 - x$$
  • C. none of these
  • D. $$\displaystyle \frac{1 - x}{2}$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer