Mathematics

# If $f(x)={ x }^{ 3 }+x,$then $\int _{ 1 }^{ 2 }{ f\left( x \right) dx+2\int _{ 1 }^{ 5 }{ { f }^{ -1 }\left( 2x \right) dx } }$

21

Its FREE, you're just one step away

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

#### Realted Questions

Q1 Single Correct Medium
Evaluate the integral
$\displaystyle \int_{0}^{a}\sqrt{a^{2}-x^{2}}dx$
• A. $\displaystyle \frac{a^{2}}{4}$
• B. $\pi {a}^{2}$
• C. $\displaystyle \frac{\pi a^{2}}{2}$
• D. $\displaystyle \frac{\pi a^{2}}{4}$

1 Verified Answer | Published on 17th 09, 2020

Q2 Subjective Medium
Integrate $\displaystyle \int \frac{x}{x^2+1}dx$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium
Evaluate : $\displaystyle \int \sqrt{\dfrac{a - x}{x}} dx$
• A. $\dfrac{\sqrt{a-x}}{\sqrt{x}}+a\tan^{-1}\left(\dfrac{\sqrt{x}}{\sqrt{a-x}}\right)+c$
• B. $\dfrac{\sqrt{a-x}}{\sqrt{x}}-a\tan^{-1}\left(\dfrac{\sqrt{x}}{\sqrt{a-x}}\right)+c$
• C. $\sqrt{a-x} \sqrt{x}-a\tan^{-1}\left(\dfrac{\sqrt{x}}{\sqrt{a-x}}\right)+c$
• D. $\sqrt{a-x} \sqrt{x}+a\tan^{-1}\left(\dfrac{\sqrt{x}}{\sqrt{a-x}}\right)+c$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Medium
Let $f : R \rightarrow R$ be a function as $f(x) = (x - 1)(x + 2)(x - 3)(x - 6) - 100$. If $g(x)$ is a polynomial of degree $\leq 3$ such that $\displaystyle \int \frac{g(x)}{f(x)} dx$ does not contain any logarithm function and $g(-2) = 10$. Then

$\displaystyle \int \frac{g(x)}{f(x)} dx$, equals
• A. $\tan^{-1} \left ( \frac{x - 1}{1} \right ) + c$
• B. $\tan^{-1} (x) + c$
• C. None of these
• D. $\tan^{-1} \left ( \frac{x - 2}{2} \right ) + c$

$\int {\dfrac{{2x + 7}}{{{{(x - 4)}^2}}}dx}$