Mathematics

# The value of $\int\limits_0^\pi {\frac{{{e^{\cos x}}}}{{{e^{\cos x}} + {e^{ - \cos x}}}}dx}$

##### ANSWER

$\frac{\pi }{2}$

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

#### Realted Questions

Q1 Subjective Medium
Integrate the function    $\cfrac {x-1}{\sqrt {x^2-1}}$

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q2 Assertion & Reason Hard
##### ASSERTION

STATEMENT-1: $\displaystyle \int_{0}^{\pi }x\:\sin\:x\cos ^{2}x\:dx=\frac{\pi }{2}\int_{0}^{\pi }\sin x\:\cos ^{2}xdx$.

##### REASON

STATEMENT-2: $\displaystyle \int_{a}^{b}x\:f(x)\:dx=\frac{a+b}{2}\int_{a}^{b}f(x)dx.$

• A. STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1.
• B. STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1.
• C. STATEMENT-1 is False, STATEMENT-2 is True.
• D. STATEMENT-1 is True, STATEMENT-2 is False.

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Hard
Let f be a function defined for every x, such that f'' = -f ,f(0)=0, f' (0) = 1, then f(x) is equal to
• A. tanx
• B. $e^{x}-1$
• C. 2sinx
• D. sinx

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q4 TRUE/FALSE Medium
state whether given statement is true or false??
$\int^{x}_{0}\left(\int^{u}_{0}f(t)dt\right)$ $du=\int^ {x}_{0}f(u).(x-u)du$
• A. False
• B. True

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020

Q5 Passage Medium
Let $F: R\rightarrow R$ be a thrice differential function. Suppose that $F(1) = 0, F(3) = -4$ and $F'(x)<0$ for all $x\in\left(\dfrac{1}{2},3\right)$. Let $f(x) = xF(x)$ for all $x\in R$.

Asked in: Mathematics - Integrals

1 Verified Answer | Published on 17th 09, 2020