Mathematics

# Evaluate the following integrals :$\displaystyle\int_{0}^{\pi}x\sin x\cos^{4}x\ dx$

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

#### Realted Questions

Q1 Subjective Hard
Solve
$I=\displaystyle \int{\dfrac{1}{\sqrt{21+4x-4x^{2}}}dx}$

1 Verified Answer | Published on 17th 09, 2020

Q2 Single Correct Medium
The value of the integral $\displaystyle \int^{1/\sqrt{3}}_{1/\sqrt{3}} \dfrac{x^4}{1-x^4} cos ^{-1} \dfrac{2x}{1+x^2} dx$
• A. $\dfrac{\pi}{\sqrt{3}} + log \dfrac{\sqrt{3} +1}{\sqrt{3} -1}$
• B. $\dfrac{1}{\sqrt{3}} + \dfrac{\pi}{2} log \dfrac{\sqrt{3} +1}{\sqrt{3} -1}$
• C. none of these
• D. $0$

1 Verified Answer | Published on 17th 09, 2020

Q3 Subjective Medium
Obtain as the limit of sum $\displaystyle\overset{log_e^7}{\underset{log_e^3}{\displaystyle\int}}e^xdx$.

1 Verified Answer | Published on 17th 09, 2020

Q4 One Word Hard
If $f\left(x\right)=\dfrac{{e}^{x}}{1+{e}^{-x}},\,\,\,{I}_{1}=\displaystyle\int_{f\left(-a\right)}^{f\left(a\right)}{xg\left(x\left(1-x\right)\right)dx},\,\,\,{I}_{2}=\displaystyle\int_{f\left(-a\right)}^{f\left(a\right)}{g\left(x\left(1-x\right)\right)dx}$ then $\dfrac{{I}_{2}}{{I}_{1}}$

1 Verified Answer | Published on 17th 09, 2020

Q5 Single Correct Medium
$\displaystyle \int \dfrac{2x\log(1+x^2)}{1+x^2}dx$
• A. $\log(1+x^2)+c$
• B. $2\log(1+x^2)+c$
• C. none of these
• D. $\dfrac{[\log(1+x^2)]^2}{2}+c$