Mathematics

# If $f\left (\dfrac {x - 4}{x + 2}\right ) = 2x + 1, (x\epsilon R - \left \{1, -2\right \})$m then $\int f(x) dx$ is equal to(where $C$ is a constant of integration).

$12\log_{e}|1 - x| - 3x + C$

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Single Correct Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 84

#### Realted Questions

Q1 Subjective Medium
Using definite integration, find area of the triangle with vertices at A(1,1),B(3,3)A(1,1),B(3,3).

1 Verified Answer | Published on 17th 09, 2020

Q2 Matrix Hard
Match the following :
 The number of polynomials f(x) non-negative integer coefficients of degree $\leq$ 2, satisfying $f(0)=0$ and $\int_{0}^{1}f(x)dx = 1$, is 8 The number of points in the interval $\displaystyle [- \sqrt{13}, \sqrt{13}]$ at which $f(x) = sin(x^2)+cos(x^2)$ attains its maximum value, is 2 $\displaystyle \int_{-2}^{2} \frac{3x^2}{(1 + e^x)}dx$ equals 4 $\displaystyle \frac{\left ( \int_{-1/2}^{1/2} cos 2x\cdot log \left (\frac{1+x}{1-x} \right )dx\right )}{\left ( \int_0^{1/2} cos 2 x \cdot log \left ( \frac{1+x}{1-x} \right ) dx \right )}$ equals NA

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium
If $\int _{ 0 }^{ 100 }{ f\left( x \right) dx=a }$, then $\sum _{ r=1 }^{ 100 }{ \int _{ 0 }^{ 1 }{ (f\left( r-1+x \right) dx) } } =$
• A. a
• B.
• C. 10a
• D. 100a

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Hard
$\displaystyle \int { { e }^{ x }\frac { \left( { x }^{ 2 }+1 \right) }{ { \left( x+1 \right) }^{ 2 } } dx } =$
• A. $\displaystyle \left( \frac { x+1 }{ x-1 } \right) { e }^{ x }+c$
• B. ${ e }^{ x }\left( x+1 \right) \left( x-1 \right) +c$
• C. none of these
• D. $\displaystyle \left( \frac { x-1 }{ x+1 } \right) { e }^{ x }+c$

$\int {\dfrac {\cos 2x}{\sin x}}dx$