Mathematics

# $\int\limits_{ - 1}^1 {{e^x}dx} =$

##### SOLUTION
We know that  $\int{e^x}dx=e^x$

$\Rightarrow \int\limits_{-1}^{1} e^x dx=[e^x]^{1}_{-1}$

$\Rightarrow e^1-e^{-1}$

$\Rightarrow e-\dfrac{1}{e}$

By taking L.C.M we get,

$\Rightarrow \dfrac{e^2-1}{e}$

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Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 109

#### Realted Questions

Q1 Single Correct Medium
If $\displaystyle I=\int \frac{dx}{\sqrt{\left ( 1-x \right )\left ( x-2 \right )}},$ then $I$ is equal to
• A. $\displaystyle \sin^{-1}\left ( 2x+5 \right )+C$
• B. $\displaystyle \sin^{-1}\left ( 3-2x \right )+C$
• C. $\displaystyle \sin^{-1}\left ( 5-2x \right )+C$
• D. $\displaystyle \sin^{-1}\left ( 2x-3 \right )+C$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
$\displaystyle \int^{\pi/2}_0\displaystyle\frac{\sin^n\theta}{\sin^n\theta +\cos^n\theta}d\theta$ is equal to:
• A. $1$
• B. $0$
• C. $\displaystyle\frac{\pi}{2}$
• D. $\displaystyle\frac{\pi}{4}$

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium
Evaluate the following integrals : $\int \dfrac{x^{2}}{x^{4}+x^{2}+1}dx$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Medium
(A) : $\displaystyle \int e^{x}(\log x+x^{-2})dx={ e }^{ x }\left( \log x-\frac { 1 }{ x } \right) +c$
(R): $\displaystyle \int e^{x}[f(x)+f'(x)]dx=e^{x}f(x)+c$
• A. Both A and R are true but R is not correct explanation of A
• B. A is true but R is false
• C. A is false but R is true.
• D. Both A and R are true and R is the correct explanation of A

Given that for each $\displaystyle a \in (0, 1), \lim_{h \rightarrow 0^+} \int_h^{1-h} t^{-a} (1 -t)^{a-1}dt$ exists. Let this limit be $g(a)$
In addition, it is given that the function $g(a)$ is differentiable on $(0, 1)$