Mathematics

# Evaluate:$\displaystyle \int_{\pi/4}^{3\pi/4} \dfrac{dx}{1+\cos x}$

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

#### Realted Questions

Q1 Subjective Medium
$\displaystyle \int { { e }^{ 3\log { x } }{ \left( { x }^{ 4 }+1 \right) }^{ -1 } } dx=$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
Evaluate : $\displaystyle \int\left(\sqrt{\frac{a+x}{a-x}}+\sqrt{\frac{a-x}{a+x}}\right)dx$
• A. $2\sin^{-1}\left(\dfrac{x}{a}\right)+c$
• B. $2\cos^{-1}\left(\dfrac{x}{a}\right)+c$
• C. $2a\,\cos^{-1}\left(\dfrac{x}{a}\right)+c$
• D. $2a\, \sin^{-1}\left(\dfrac{x}{a}\right)+c$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Medium
The integral $\displaystyle\int \dfrac{2x^3-1}{x^4+x}dx$ is equal to?(Here C is a constant of integration)
• A. $\dfrac{1}{2}log_e\dfrac{(x^3+1)^2}{|x^3|}+C$
• B. $\dfrac{1}{2}\log_e\dfrac{|x^3+1|}{x^2}+C$
• C. $log_e\dfrac{|x^3+1|}{x^2}+C$
• D. $\log_e\left|\dfrac{x^3+1}{x}\right|+C$

1 Verified Answer | Published on 17th 09, 2020

Q4 Subjective Medium
Evaluate the definite integral   $\displaystyle \int_0^{\tfrac {x}{4}}\sin 2x dx$

Consider two differentiable functions $f(x), g(x)$ satisfying $\displaystyle 6\int f(x)g(x)dx=x^{6}+3x^{4}+3x^{2}+c$ & $\displaystyle 2 \int \frac {g(x)dx}{f(x)}=x^{2}+c$. where $\displaystyle f(x)>0 \forall x \in R$