Mathematics

Evaluate the integral $$\displaystyle \int_{3}^{5}(2-x)dx$$.


SOLUTION
Consider, $$I=\displaystyle \int_{3}^{5}(2-x)dx$$

$$\Rightarrow$$ $$I=\left[2x-\dfrac {x^2}2\right]_3^5$$

$$\Rightarrow$$ $$I=10-\dfrac {25}2-6+\dfrac 92$$

$$\Rightarrow$$ $$I=4-8=-4$$
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:

$$\int x.\sin{2x}dx$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q2 Subjective Medium
$$\int{\dfrac{dx}{{x}^{1/3}+{x}^{1/2}}}$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q3 Single Correct Medium
$$\displaystyle \int\frac{1-\sqrt{x}}{1+\sqrt[4]{x}}dx=$$
  • A. $$ x+\displaystyle \dfrac{4}{5}x^{5/4}+c$$
  • B. $$ x-\displaystyle \dfrac{2}{5}x^{5/4}+c$$
  • C. $$ x-\displaystyle \dfrac{3}{5}x^{5/4}+c$$
  • D. $$ x-\displaystyle \dfrac{4}{5}x^{5/4}+c$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q4 Single Correct Medium
The value of $$\int_{0}^{2}\dfrac{dx}{(17+8x-4x^2)(e^{6(1-x)}+1)}$$ is equal to
  • A. $$-\dfrac{1}{8\sqrt{21}}\log \left | \dfrac{2-\sqrt{21}}{2+\sqrt{21}} \right |$$
  • B. $$-\dfrac{1}{8\sqrt{21}}\log \left | \dfrac{2+\sqrt{21}}{\sqrt{21}-2} \right |$$
  • C. $$-\dfrac{1}{8\sqrt{21}}\left \{ \log \left | \dfrac{2-\sqrt{21}}{2+\sqrt{21}}\right |-\log \left | \dfrac{2+\sqrt{21}}{\sqrt{21}-2} \right | \right \}$$
  • D. None of these

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q5 Single Correct Medium
Solve: $$\displaystyle \int\dfrac{1}{x(x^{4}-1)}dx$$
  • A. $$-\dfrac{1}{4}\ln\left|\dfrac{x^{4}-1}{x^{4}}\right|+c$$
  • B. $$-\dfrac{1}{4}\ln\left|\dfrac{x^{2}-1}{x^{2}}\right|+c$$
  • C. $$\dfrac{1}{4}\ln\left|\dfrac{x^{2}-1}{x^{2}}\right|+c$$
  • D. $$\dfrac{1}{4}\ln\left|\dfrac{x^{4}-1}{x^{4}}\right|+c$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer