Mathematics

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

##### SOLUTION
Consider,
$I=\displaystyle\int_{0}^{2} 3x+2\ dx$

$=\left[ 3\dfrac{x^2}2+2x \right]_0^2$

$\Rightarrow$$6+4-0-0=10$

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

#### Realted Questions

Q1 Single Correct Hard
Evaluate $\displaystyle\int{\frac{{(x+\sqrt{1+x^2})}^{15}}{\sqrt{1+x^2}}dx}$.
• A. $\displaystyle\frac{{(x+\sqrt{1+x^2})}^{14}}{14}+C$
• B. $\displaystyle\frac{{(x+\sqrt{1+x^2})}^{16}}{16}+C$
• C. $\displaystyle\frac{{(x+\sqrt{1+x^2})}^{17}}{17}+C$
• D. $\displaystyle\frac{{(x+\sqrt{1+x^2})}^{15}}{15}+C$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
$I = \int_0^1 {{e^{{x^2}}}dx \Rightarrow }$
• A. $I \ge 0$
• B. $I \le 0 \le e$
• C. $I > 4$
• D. $I \ge e$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Hard
Solve: $\displaystyle \int \dfrac{\sin 2x}{\sin \left(x - \dfrac{\pi}{4}\right) .\sin \left(x + \dfrac{\pi}{4}\right)} dx$
• A. $\log\left |\sin^2 x + \dfrac{1}{2}\right|$
• B. $\log\left |\sin x - \dfrac{1}{2}\right|$
• C. $\log\left |\sin^2 x + \dfrac{1}{\sqrt{2}}\right|$
• D. $\log\left |\sin^2 x - \dfrac{1}{2}\right|$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
Integrate :-
$\displaystyle \int_{}^{} {\frac{{dx}}{{x\left( {x + 1} \right)}}}$

Solve $\displaystyle\int {\dfrac{x}{{\sqrt {4 - {x^2}} }}} dx$