Mathematics

Evaluate: $$\int { 5-4x-{ x }^{ 2 } } dx$$.


SOLUTION
$$\displaystyle \int(5-4x-x^2)dx$$

$$\displaystyle = \int 5dx-\int 4xdx-\int x^2dx$$

$$\displaystyle = 5\int dx-4\int xdx-\int x^2dx$$

$$\displaystyle =5x-4\cdot \dfrac{x^2}{2}-\dfrac{x^3}{3}+C$$

$$=5x-2x^2-\dfrac{x^3}{3}+C$$
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 114
Enroll Now For FREE

Realted Questions

Q1 Single Correct Hard
Statement-l $$\displaystyle \int_{0}^{\pi/2}\frac{dx}{1+\tan^{5}x}=\frac{\pi}{4}$$

Statement 2:$$\displaystyle \int_{0}^{a}f(x)dx=\int_{0}^{a}f(a+x)dx= \int_{0}^{\pi/2}\displaystyle \frac{dx}{1+\tan^{3}x}=\int_{0}^{\pi/2}\displaystyle \frac{d_{X}}{1+\cot^{3}x}=\frac{\pi}{4}$$
  • A. Statement 1 is True, Statement 2 is True; Statement 2 is a correct exlanation for Statement 1
  • B. Statement 1 is True, Statement 2 is True; Statement 2 Not a correct exlanation for Statement 1
  • C. Statement 1 is False, Statement 2 is True
  • D. Statement 1 is True, Statement 2 is False

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q2 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
Q3 Single Correct Hard
Suppose $$\displaystyle A=\int{\frac{dx}{x^2+6x+25}}$$ and $$\displaystyle B=\int{\frac{dx}{x^2-6x-27}}$$. If $$\displaystyle 12(A+B)=\lambda.\tan^{-1}{\left(\frac{x+3}{4}\right)}+\mu.\ln{\left|\frac{x-9}{x+3}\right|}+C$$, then the value of $$(\lambda+\mu)$$ is $$\dots$$.
  • A. $$1$$
  • B. $$2$$
  • C. $$3$$
  • D. $$4$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q4 Subjective Hard
Prove that : $$\displaystyle \int_{0}^{1} \tan^{-1} x dx = \dfrac {\pi}{4} - \dfrac {1}{2}\log 2$$.

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q5 Subjective Easy
$$\int \frac{2x^{2}}{3x^{4}2x} dx$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer