Mathematics

# Integrate with respect to $x$.:$e^{x}(\text{sec}^2 {x}+\tan x)$

##### SOLUTION
$\int e^{x} (f(x)+ f (x))dx = e^{ x} f (x)$
$\Rightarrow \int e^{x} (\tan + \sec^{2} x)= e^{x} \tan x +c$

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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 Medium
If $\displaystyle \frac{dI}{dy}=3^{\cos y}.\sin y$ then $I$ is equal to
• A. $\displaystyle 3^{\cos y}+c$
• B. $\displaystyle \sin y+c$
• C. $3^{\sin y}+c$
• D. $\displaystyle - \dfrac{3^{\cos y}}{\log 3}+c$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
Value of $\displaystyle \int_{1}^{5} \left(\sqrt {x+2\sqrt {x-1}}+\sqrt {x-2(x-1)}\right)dx$ is
• A. $\dfrac {16}{3}$
• B. $\dfrac {32}{3}$
• C. $\dfrac {34}{3}$
• D. $\dfrac {8}{3}$

1 Verified Answer | Published on 17th 09, 2020

Q3 Multiple Correct Hard
The value of the integral $\displaystyle \int_{0}^{\pi /2}\frac{\sqrt{\cot x}}{\sqrt{\cot x}+\sqrt{\tan x}}dx$ is
• A. $\displaystyle \pi /2$
• B. $\displaystyle \int_{\pi /8}^{3\pi/8 }\frac{\sqrt{\cot x}}{\sqrt{\cot x}+\sqrt{\tan x}}dx$
• C. $\displaystyle \pi /4$
• D. $\displaystyle \int_{0}^{\pi /2}\frac{dx}{1+\tan ^{3}}x$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Medium

The value of $\displaystyle \int_1^e {\frac{1}{x}(1 + \log x)dx}$ is

• A. $\displaystyle \frac{1}{2}$
• B. e
• C. $\displaystyle \frac{1}{e}$
• D. $\displaystyle \frac{3}{2}$

The average value of a function f(x) over the interval, [a,b] is the number $\displaystyle \mu =\frac{1}{b-a}\int_{a}^{b}f\left ( x \right )dx$
The square root $\displaystyle \left \{ \frac{1}{b-a}\int_{a}^{b}\left [ f\left ( x \right ) \right ]^{2}dx \right \}^{1/2}$ is called the root mean square of f on [a, b]. The average value of $\displaystyle \mu$ is attained id f is continuous on [a, b].