Mathematics

Evaluate $$\int {{r^4}\left( {7 - \dfrac{{{r^5}}}{{10}}} \right)} \,dr$$


SOLUTION
$$I=\displaystyle\int r^4\left(7-\dfrac{r^5}{10}\right)dr$$

$$=\displaystyle\int \left(7r^4-\dfrac{r^9}{10}\right)dr$$

$$=7\displaystyle\int r^4dr-\dfrac{1}{10}\displaystyle\int r^9dr$$

$$=\dfrac{7}{5}r^5-\dfrac{1}{100}r^{10}+c$$.
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 the following definite integral:

$$\displaystyle\int_{1}^{2} \dfrac 2x\ dx$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q2 Subjective Medium
Write a value of 
$$\int { \sqrt { { x }^{ 2 }-9 }  } \  dx\quad $$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q3 Single Correct Medium
$$\displaystyle \int\cos^{-3/7}x\sin^{-11/7}xdx$$ is equal to
  • A. $$\log|\sin^{4/7}x|+c$$
  • B. $$ \displaystyle \frac{4}{7}\tan^{4/7}x+c$$
  • C. $$ \log|\cos^{3/7}x|+c$$
  • D. $$ -\displaystyle \frac{7}{4}\tan^{-4/7}x+c$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q4 Single Correct Hard
If $$\phi \left( x \right) = {\int {\left\{ {\phi \left( x \right)} \right\}} ^{ - 2}}dx$$ and $$\phi \left( 1 \right) = 0$$ then $$\phi \left( x \right) = $$
  • A. $${\left\{ {2\left( {x - 1} \right)} \right\}^{\frac{1}{4}}}$$
  • B. $${\left\{ {5\left( {x - 2} \right)} \right\}^{\frac{1}{5}}}$$
  • C. none of these
  • D. $${\left\{ {3\left( {x - 1} \right)} \right\}^{\frac{1}{3}}}$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q5 Subjective Medium
Evaluate: $$\displaystyle \overset{\pi/2}{\underset{0}{\int}} \sin x\cdot \sin 2x \,\,dx$$.

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer