Mathematics

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

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

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

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

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

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

Its FREE, you're just one step away

Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 114

#### 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

1 Verified Answer | Published on 17th 09, 2020

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

1 Verified Answer | Published on 17th 09, 2020

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. $4$

1 Verified Answer | Published on 17th 09, 2020

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

$\int \frac{2x^{2}}{3x^{4}2x} dx$