Mathematics

If $(-1, 2)$ and $(2, 4)$ are two points on the curve $y=f(x)$ and if $g(x)$ is the gradient of the curve at point (x, y), then the value of the integral $\displaystyle\int^{2}_{-1}g(x)dx$, is?

$2$

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Single Correct Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 86

Realted Questions

Q1 Single Correct Hard
$\displaystyle\int { \sin ^{ -1 }{ \sqrt { \dfrac { x }{ a+x } } } dx }$ is equal to
• A. $\left[ \tan ^{ -1 }{ \sqrt { \dfrac { x }{ a } } } +\sqrt { \dfrac { x }{ a } } \right] +C$
• B. $a\left[ \tan ^{ -1 }{ \sqrt { \dfrac { x }{ a } } } -\sqrt { \dfrac { x }{ a } } \right] +C$
• C. $a\left[ \tan ^{ -1 }{ \sqrt { \dfrac { x }{ a } } } \cdot \dfrac { \left( a+x \right) }{ a } \right] +C$
• D. $a\left[ \tan ^{ -1 }{ \sqrt { \dfrac { x }{ a } } } \cdot \dfrac { \left( a+x \right) }{ a } -\sqrt { \dfrac { x }{ a } } \right] +C$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
Solve $\int { (\log_ e x)^2} dx$ o
• A. $x \log_e x (\log_e x +2)+c$
• B. $x \log_e(2\log_e \ x + 1)+c$
• C. $x\{(\log_e x )^2 - 2(log_ex-2)\}+c$
• D. $x[(\log x)^2 - 2(\log x)+2] + c$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium
The value of $\displaystyle \int \dfrac {e^x}{x} ( x \log x+1) \ dx$  is equal to
• A. $\dfrac {e^x} {x} + C$
• B. $x e^x \log |x| + C$
• C. $x ( e^x + \log |x| ) + C$
• D. $xe^x + \log |x| + C$
• E. $e^x \log |x| + C$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Hard
The value of the integral $\displaystyle \int_{\pi}^{2\pi}\dfrac {(x^{2} + 2)\cos x}{x^{3}}dx$ is
• A. $-\left (\dfrac {1}{4\pi^{2}}\right )$
• B. $\dfrac {1}{4\pi^{2}}$
• C. $\dfrac {5}{4\pi^{2}}$
• D. $-\left (\dfrac {5}{4\pi^{2}}\right )$

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