Mathematics

# ${\int}_{0}^{a}\left[f\left(a+x\right)+f\left(a-x\right)\right]dx=$

${\int}_{-a}^{a}f(x)dx$

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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 Hard
Evaluate:  $\displaystyle \int_{0}^{\pi/ 2} \frac{\sin^2x}{\sin x+\cos x}dx$.

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
What is $\displaystyle \int_{0}^{2\pi}\sqrt {1 + \sin \dfrac {x}{2}}dx$ equal to?
• A. $4$
• B. $2$
• C. $0$
• D. $8$

1 Verified Answer | Published on 17th 09, 2020

Q3 Single Correct Hard
$\int \dfrac{(x+1)}{x(1+xe^{x})^{2}}dx$ is equal to
• A. $ln \left|\dfrac{xe^{x}}{1+xe^{x}}\right|+\dfrac{1}{1+xe^{x}}+C$
• B. $\dfrac{1}{1+xe^{x}}+C$
• C. $x+ln \left|\dfrac{x}{1+xe^{x}}\right|+\dfrac{1}{1+ex^{x}}+C$
• D. $ln \left| \frac{ xe^{ x } }{ 1+xe^{ x } } \right| +C$

1 Verified Answer | Published on 17th 09, 2020

Q4 Single Correct Medium
The integral $\displaystyle \int \frac{2x^{12} + 5x^9}{(x^5 + x^3 + 1)^3} dx$ is equal to :
where, C is an arbitrary constant.
• A. $\frac{- x^5}{(x^5 + x^3 + 1)^2} + C$
• B. $\frac{x^5}{(x^5 + x^3 + 1)^2} + C$
• C. $\frac{- x^{10}}{2(x^5 + x^3 + 1)^2} + C$
• D. $\frac{x^{10}}{2(x^5 + x^3 + 1)^2} + C$

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 $\displaystyle f(x)>0 \forall x \in R$