Mathematics

# $\displaystyle\int_{0}^{2} 3x+2\ dx$

##### SOLUTION

Given  $\displaystyle\int_{0}^{2} 3x+2\ dx$

$=\left. 3\dfrac{x^2}2+2x \right]_0^2$  [$\because \displaystyle\int x^n=\dfrac{x^{n+1}}{n+1}$]

$=6+4-0-0$

$=10$

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

#### Realted Questions

Q1 Single Correct Hard
Solve:-
$\int\limits_0^1 {\frac{{dx}}{{{{({x^2} + 1)}^{3/2}}}}}$
• A. $1$
• B. $\sqrt 2$
• C. $\dfrac{1}{\sqrt 2}$
• D. $1/2$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
The integral $\int_{2}^{4}{\frac {log x^{2}}{log x^{2} +log (36-12x+x^{2})}} dx$ is equal to :
• A. 6
• B. 2
• C. 4
• D. 1

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Hard
Evaluate $\displaystyle \int \sqrt{\frac{1+x}{x}}dx.$
• A. $\displaystyle =\sqrt{x^{2}-x}+\frac{1}{2}\log \left | \left ( x+\frac{1}{2} \right )+\sqrt{x^{2}+x} \right |+C$
• B. $\displaystyle =\sqrt{x^{2}-x}+\frac{1}{2}\log \left | \left ( x-\frac{1}{2} \right )+\sqrt{x^{2}+x} \right |+C$
• C. $\displaystyle =\sqrt{x^{2}+x}+\frac{1}{2}\log \left ( \left ( x+\frac{1}{2} \right )+\sqrt{x^{2}+x} \right )+C$
• D. $\displaystyle =\sqrt{x^{2}+x}+\frac{1}{2}\log \left | \left ( x+\frac{1}{2} \right )+\sqrt{x^{2}+x} \right |+C$

1 Verified Answer | Published on 17th 09, 2020

Q4 Assertion & Reason Medium
##### ASSERTION

If $D(x)\, =\,\begin{vmatrix} f_{1}(x) & & f_{2}(x) & & f_{3}(x) & \\ a_{2} & & b_{2} & & c_{2} & \\ a_{3} & & b_{3} & & c_{3} & \end{vmatrix}$ , where
$f_{1}$,$f_{2}, f_{3}$ are differentiable function and $a_{2},\, b_{2},\, c_{2},\, a_{3},\, b_{3},\, c_{3}$ are constants then
$\int D(x)dx\,=\, \begin{vmatrix}\int f_{1}(x)dx & & \int f_{2}(x)dx & & \int f_{3}(x)dx & \\ a_{2} & & b_{2} & & c_{2} & \\ a_{3} & & b_{3} & & c_{3} & \end{vmatrix}\, +\, C$

##### REASON

Integration of sum of several function is equal to sum of integration of individual functions.

• A. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• B. Assertion is correct but Reason is incorrect
• C. Assertion is incorrect but Reason is correct
• D. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

Let $\displaystyle f\left ( x \right )=\frac{\sin 2x \cdot \sin \left ( \dfrac{\pi }{2}\cos x \right )}{2x-\pi }$