Mathematics

Evaluate :
$$\int { \left( 1-x \right) \sqrt { x }  } dx$$


SOLUTION
$$I=\displaystyle\int{\sqrt{x}dx}-\displaystyle\int{x\sqrt{x}dx}$$

$$=\displaystyle\int{{x}^{\frac{1}{2}}dx}-\displaystyle\int{{x}^{1+\frac{1}{2}}dx}$$

$$=\displaystyle\int{{x}^{\frac{1}{2}}dx}-\displaystyle\int{{x}^{\frac{3}{2}}dx}$$

$$=\dfrac{{x}^{\frac{1}{2}+1}}{\dfrac{1}{2}+1}-\dfrac{{x}^{\frac{3}{2}+1}}{\dfrac{3}{2}+1}$$

$$=\dfrac{2x\sqrt{x}}{3}-\dfrac{2{x}^{2}\sqrt{x}}{5}+c$$
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
$$\int {\frac{{dx}}{{\sqrt {2 - 4x + {x^2}} }}} $$=?

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q2 Subjective Medium
$$\int (x+1)^2 dx$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q3 Single Correct Medium
$$\displaystyle \int[\frac{cosx}{x}-\sin{x}\log x]dx=$$
  • A. $$ (\log x) sinx+c$$
  • B. $$2(\log x) (cos x) +c$$
  • C. $$-(\log x) sin x+c$$
  • D. $$(\log x) (cos x) +c$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q4 TRUE/FALSE Hard
$$\displaystyle \int_0^{\pi} sin x =\displaystyle \lim_{n \rightarrow \infty} \displaystyle \Sigma_{i=1}^n sin \left(\dfrac{\pi i}{n}\right) \dfrac{\pi}{n}$$
State whether the above statement is True or False?
  • A. False
  • B. True

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q5 Single Correct Medium
Evaluate $$\int {{e^x}\left( {\dfrac{1}{x} - \dfrac{1}{{{x^2}}}} \right)} \,dx$$
  • A. $$\dfrac {e^x}{x^2}+C$$
  • B. $$-\dfrac {e^x}{x^2}+C$$
  • C. $$-\dfrac {e^x}{x}+C$$
  • D. $$\dfrac {e^x}{x}+C$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer